Here's a list of some open source game engines in general. You'll want to look at the cross-platform, 2D-oriented engines and see which one best meets your needs as far as programming language and features.
However, PyGame is pretty well-developed, and Python is an exceptionally easy and fun language to do anything in, including game development. I recommend you check out PyGame first, I think it would work well for your task.
As for developing flash games on Linux, there's little chance of that. To develop flash games you need Adobe's suite, and it is only compatible with Windows and Mac. So unless your computer can handle the stress of Adobe software (which is pretty high) in an emulated environment (Wine, which adds considerable hardware overhead), you'd need Windows or Mac OS X to do that. You can still play them, however.