Well, all the games here are made in flash, but it's expensive (699$) and difficult to use. If you want to do it just for fun, try game maker or the games factory 2.
If you want to make an fps in flash the you might want to get the unity engine. If it's just a simple on than you can just make your own engine or not. A strategy games is relatively simple once you have all the logic and AI in place and it's a tile based one.
Hi Darkroot! I have a question. On your last post you mentioned that he should use unity to make an fps in flash? Unity can make flash games? Wow, didn't know that. If that's the case, I think it might be worth a look at. Shiva only has LUA.
Yes, the unity engine has been ported to flash and a bunch of platforms now. First unity game I've seen was interstellar marines but Kongregate had/has a contest with the engine. It's a pretty cool and powerful 3d engine.
