I would absolutely allow a 10 year old to make that choice. After all, she is the one who suffered with the flu last year, and she wants to avoid repeating that experience.
Nothing strange about that. And you can say "Hey, the shot doesn't always work, so it's not a guarantee, but if you choose this I won't stop you"
And what if you don't allow her to get it and she contracts the flu again? She could really hold that against you, I would think.
At 10 I think a...