Look at brother's farewell team instance. Water's dodge is similar to the one of medical ninjas there. Same as iruka's dodge (although he can dodge only once). You will notice that at certain point your attacks always hit or almost always miss the target, which indicates that some stat (combo rate? There's no stat directly responsible for "hit rate") influences whether you will dodge or not. When I was doing brothers farewell TI around 80-100k bp medics could dodge hits, nowadays it literally never happens. Same with iruka, iruka roughly on my power dodges, while ~30-40k weaker one almost never dodges.

Ah, and no matter what you cant dodge undodgeable mysteries/standards.

So once we have a rough idea how it works, it can trigger with standards, mysteries and aoe chases (in all cases thats the first damaging effect that hits main). Not sure if it can trigger in the middle of chase chain, but such mechanic was already in the game in 2.0 (old kage minato dodge), you might want to do some tests with friends like main vs main on similar power just to see what happens.

tl;dr it seems to be 40% to dodge any incoming damage/effect and can be triggered up to 2 times. It doesnt neccessarily have to be 1st and 2nd attack.