Most of the coaches I have met weren't just childhood skaters, but were competitive childhood skaters. It makes sense. There are so many ex-competitive skaters that a figure skating director or skating student can easily choose someone with an impressive sounding background. Another thing is that people who have a dance, gymnastics, skating, or similar area background somehow seem to move more smoothly than those who do not. I'm not sure that is something you really can pick up as an adult. I don't even understand exactly what the difference is, but anyone can see it.
Around Washington, DC, to be hired or allowed to coach at a rink, you pretty much have to be silver test level, gold test at some rinks. But that is a big city. I would guess you might be able to teach in a small town, maybe at an outdoor rink, with less qualification.
That said, I had a coach (Barbara McDonnell Walker;
http://icedancepro.com) who I think started as an adult. But she was very athletic (I don't know her previous background, but she couldn't possibly have learned to be that good without childhood athletics) - and she mostly focussed on ice dance.
I knew a coach at a local rink who took an adult dancer and teacher (Ballet?) under her wing to become a coach, because skating coaches can earn more. Again, a very athletic background, in a related area.
I once met a former ballerina (from a dance troupe with "National" in the name) who was practicing triple axels after skating for just 10 months, at a time when triple axels were quite uncommon among even the best lady competitors. (She said she'd done triple jumps in ballet, which probably implies she was a "principal dancer", playing lead roles, maybe even a prima ballerina - an extremely select group. The fraction of girls who take ballet lessons as a child who become national troup principal dancers may well be less than the fraction of kids who take LTS lessons who go on to win Olympic gold medals, because so many little girls take ballet lessons . I.E., she was already an extremely elite athlete in an extremely competitive field, quite possibly a better athlete than many or most of the Olympic medalists.) I don't know that she ever coached, and I don't know how good a skater she was doing anything else. But I have no doubt she could have - she did a good job of explaining the difference between ballet and skating style jumps. I think she could have done anything athletic she wanted. But again - an extremely athletic childhood related-area background.
There are also some people here who teach off-ice classes aimed at skaters, often at skating rinks. Yoga. Ballet. Ballroom dance. (E.g., "Ballet For Figure Skaters".) Perhaps it would be easier to do that?
Volunteering is different from paid coaching - at Fort Dupont, in Washington, DC, some hockey skaters with no figure skating background volunteer to coach LTS figure skating classes. Even I have taught there.
I'm no expert, but here is some of what I learned from volunteering, which is a very good way to learn about teaching kids:
As other people have indicated, iIf you run into a problem teaching something, or getting people's attention, ask here for advice. Also, ask the more experienced coaches in the program. Some of the best volunteer coaches have a school teacher background. They know how to handle kids. Keeping the attention and some level of discipline is something school teachers have spent a lot of time learning, and have to be very good at. I always had a problem with discipline - I don't like to talk strictly, and sometimes you have to. Sometimes you even have to threaten to kick a kid out of class, and sometimes you even have to do it. I completely hated that. I also tried too hard to deal with the kids who had trouble with the basics - the figure skating director told me to focus on the better kids more. It's something you have to do in a large class setting, if you don't want to bore the better students.
Just accept that most of the kids will drop out by Basic 3, maybe earlier. That's also about the level at which most programs make most students go through each class more than once. Up through Basic 2, if the kids sort of get it, and they attend most of the classes, and get there on time, they are allowed to pass, in most programs.
You will also come to realize that most of the younger kids don't respond well to words used to teach motions. They are mostly monkey-see-monkey-do, and don't associate words and analysis with movement. Which is very different from most adults, though some of the most athletic adults are the same way. Some of the kids learn best by being physically guided through a motion - but be careful. Touching kids should be avoided if you can - especially in today's climate. To many people, it doesn't look right, no matter how innocent. So try to find another way to teach them.
You will need to compromise regarding kids who habitually come late or miss lessons, which happens a lot: usually their parents are at fault, but that still isn't something you can fix. You can do things like teach the skills in reverse order on alternate days, but in the end, if a student isn't there to learn when you teach, you have to accept that you can't solve everyone's problems.
Then there is the sibling problem: they need to be separated. They want to spend all their time annoying each other instead of learning. Some hockey boys, whose parents made them taking figure skating lessons, but who have no interest, and are also much better skaters in some ways than the true beginners, want to annoy all the girls instead. You may have to give up on them, but you need to make sure they don't disrupt learning for ones they want to pick on. The ones that disrupt learning for the others are prime candidates for being kicked out of that day's class, as horrible as that sounds.
You will also have to learn to respond to questions and interactions from kid's parents and other guardians, before or after the lesson. I finally decided that it is best to move the class far from the parents during the lesson, and to get the kids to face away from their parents, because parents don't understand how distracting it can be to try to get their kids' attention during class. I'm not sure if that can apply as much to private lesson students, which I never had, because those parents pay more money, and might feel they have bought your attention, but it seems to me that all the REAL coaches do it to some extent. You can't expect a kid to give their attention to you and to their parent(s), guardians, or siblings, at the same time.
Most of the kids (or adult) who have a lot of trouble with balance simply haven't tied their laces tight, or their parents haven't. You don't have time during a lesson to retie them all - but sometimes there is little choice with a particular child who keeps falling down. I would guess that 5-10% of students in the beginning classes will have their shoes tied as tight as they should be, but that's life - and the reason a lot of them won't be able to move past basic 2.
If I had a choice in the matter, I would have handed all my students a sheet of paper at the end of the first lesson or two explaining how important was attendance, coming on time, practicing outside class, tying laces, and listing the skills covered by the class. But the figure skating director didn't like that idea.
There are kids who don't know how to listen to adults at all. A school teacher explained it to me: it is typically a sign of parental (or guardian) neglect. E.g., children of parents on drugs. In principle, you may be supposed to do something about it, may even be legally required to do so, depending on local law. But you probably don't have the background to be certain. (In the end, I never acted, because I was never quite sure.) In practice, you can spend only so much time trying to compel those kids' attention. Maybe that is something mostly unique to the program I volunteered for - they are in an economically depressed area, where drug use is common.
One more thing. You aren't just there to teach. The kids are there to have fun. They should be encouraged, praised, and there should be some type of "game time", or something equivalent at the end of the lesson. Maybe hand out gold stars to every one who doesn't make a complete nuisance of themselves. They don't need to be perfect at things - save that for private lessons.