As it stands, I'm old school, and prefer pen and paper, but, for millennials (maybe this is too much for one app):
I love the emoticons!
Don't let me push you to work too hard on this, but:
What makes this specific to figure skating? (That's my main comment.)
Another emoticon for questions to ask coach, and requests for comment?
Sound effects?
Can you make words bold or underline?
Can you email and text progress and goals to friends, or post it on social media?
Can you receive a friend's progress and goals?
Gesture input (wave phone around in patterns - silly, but cool)?
Can you edit a past note?
Can you or your coach draw a diagram - e.g., a pattern? (Great place to use gesture input.)
Can a diagrams and comments be imported from a PC or Mac or email attachment?
Can the GPS and/or acceleratometer/gyroscope capture a skated pattern (by you or your coach), maybe with voice comments? (Maybe too hard.)
Can you capture audio/video (of you or coach)? Can you slow them down on replay?
Hear metronome and/or program music?
Voice input/output? (Easier and safer to use while skating. Kids don't stop skating while playing with their phone.)
Split screen mode for skating with VR headset?
Can you see the camera image ahead of you in the background, or hear collision warning beeps? (Probably too hard.)