There's stykz, but it's nowhere near a substitute for flash. It is free though!
Stykz - The first multi-platform stick figure animation program
Just for you.
Perhaps you'd like Pencil. I've heard some pretty good things about it, even though I've never personally used it. Here's a tutorial that a quick YouTube search brought up. If that's not right for you, check out GIMP. It's likely much more powerful, but it's also going to probably be more difficult to learn. Animation is handled by a plugin called GIMP GAP. It's extremely powerful, but you'd be well advised to look up any tutorials you can for it.
I've tried that already.
It's like my grandpa always said, "The god of death eats only an apple."