there are a lot of options,but the best free one I am aware of is Game Maker.You can not put any games not made in Flash on ArmorGames.com but if you just want to get started then you could try that.if you need a link then here I suppose...
[url]http://www.yoyogames.com/[/url]
Personally I would suggest you get the student version of Flash which is only $250 and get it as a present on a special event,such as Christmas or a Birthday if you want it bad enough,even though you still won't be able to post the games on here because of legal things concerning the student version,but you could also save up to get flash at full version as well,or get it as a present if you get enough money.Either way Game Maker is probably the standard on free gaming creating software it seems,since thats all the High Schools in my area teach for lower level game design courses.If you need any more info on any of the things I just talked about like any particular links just send me a message on my profile.
There is quite a difference between flash and a game engine. I toyed around with Tork quite some time ago, which is a 3D game engine - which was what I thought you were looking for. But, if you want to do something with flash, there's not much else other than Adobe's Flash. Once you have that, I believe there are a few things you can look at... but flash itself is definately a prerequisite.