theres a few obscure posts in this forum that even i cant remember where they are because server sided games arent popular among us hackers. server based games are usually avoided because they take so much time and effort just to do anything. if you really want to try and hack one, follow a guide for a normal game (not server sided) and then do the same thing for a server sided game. youll see what i mean.
google chrome is fine, as long as you know which process the game is using. (usually you can find it in firefox much quicker, but thats a personal preference)
cheat engine is definitely capable of it, but its limited to whatever is client sided. usually for server sided games you want to try editing packets with something like charles or wpe pro before looking in the swf.
and yes, the type of game matters. hacking flash is different than unity, which is different from html5, and so on and so forth.