The stuttering at the start is a result of chrome compiling the JavaScript in the background so it will run faster. It starts displaying the game before it's done so people can start using it quicker.
We had the debate about a native exporter a while ago, but it doesn't seem like it would be worth bothering with (C2's code execution speed is plenty fast for most games, especially on desktop, and it actually renders faster than construct classic does, which was native dx9). I really doubt it would improve stability any - google's got an army of programmers to throw at chrome, and as such it's quite stable as it is.
As for flash, it's still a capable technology, but it has a lot of problems (stability in particular, it crashes often on some people's systems/browsers), and both iOS and android don't support the flash player though AIR apps can still be made. It's steadily being replaced by html5 - even adobe seems to be basically admitting that html5 is going to take over by making tools to convert flash to html5 and discontinuing development of it for android.