There's a ton of variables there, but I'll give it a shot.
You don't say what form your illustration takes. If you work at all with traditional materials (i.e. you actually draw with pencils, pens, brushes, paints, etc.) you might not care much for Flash. That's just a hunch, of course. Everyone is different. If, however, you work in Adobe Illustrator, you could possibly make the move to Flash without much of a problem. Personally, even though much of the illustration I do is done with Illustrator, I never liked Flash. I found the whole environment far too mechanical and tedious.
How long it will take to learn Flash is unanswerable. You can learn the basics fairly quickly. But to really know it, and be able to do amazing things with it could take a good long time...like anything else. Again, personally, I found the learning curve fairly high. But, then, there was nothing about the app that kept me engaged (the way Illustrator or Photoshop do) Since you say you liked animation, you may find Flash much more appealing than I did. If so, your learning curve will probably be much more climbable. Understand, too, that knowing Flash involves much more than just the art/animation stuff. Any Flash work you get is likely going to also involve various scripting and web technologies as well. This is one reason you see a lot of developers working as Flash artists.
It's not hard to get work doing Flash. It's pretty much a requirement in any design position I've seen advertised in the past several years. However, at a beginner's level (such as yourself) the work you'd get is likely to be the most low-level stuff (ads, simple animations, etc) Certainly good fodder for learning, but also the kind of stuff (and their attendant deadlines and low pay) that can easily burn a guy out, unless he really, really wants to be a Flash guru. Additionally, Flash jockeys are plentiful. It's not like it's an untapped market. You will be competing with darn near every fresh graduate from any design program worth its reputation, as well as scads of developers armed with cracked copies of Flash.
I'm not tying to dissuade you from exploring Flash, mind you. I think a person should explore any direction they want. But, I do think anyone wanting to head into Flash needs to understand that Flash is quickly becoming a commodity talent. But, when I consider your basic plan...do Flash to fill the gaps between illustration work...it may very well be a good direction for you. If you haven't yet, go download a trial version and give it a go. You just might open a whole new door to your future.