fresnoflyman,
Check out the paddling section of the bulletin board. There are several people there that fish from kayaks. I don't have one, but I have fished from a canoe. So far we've never flipped it, at least not by accident. 
We always turn it and point into the wake of a passing boat without problem, but if the wake was to hit you in the side I think you'd flip pronto.
hope that helps,
hNt
"If we lie to the government, it's called a felony, when they lie to us, it's called politics." Bill Murray
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