As a game based on Nyan Cat, it works well enough
If you plan to do anything more with this than just "a game based on nyan cat":
- Smoother transitions - right now it just drops you into the game.
- Improve on the rainbow. It seems like you're adding sprites at the position of the player, which works well enough until you get drastic vertical or horizontal movement. Consider making each "rainbow piece" contain a link to the previous one, and moving and skewing them to get seamless transitions.
- Complexity - there's not really a difficulty curve, and there's not really any strategy involved. Consider adding an incentive to do "risky things", like flying close to bullets or flying towards the right edge of the screen.