We do a lot of plyometric-type work outs. Just put a couple spotting blocks and/or panel mats in a line on the floor/runway/anywhere there's space about two feet apart, maybe some hula hoops to jump through or across so you've built a type of obstacle course. Then, you're going to go through it several times (we do a couple sets of three times), jumping with both feet onto mats/blocks and then down and then up to the next one, all the way through your course. Again, we go through the course three times, then rest, and do it again. If that's too easy, even after several sets, try doing one foot at a time. This will also help your height in tumbling.
Another thing is to do jumps (straight, tuck, etc) on a mat (a squishy 8" works, or a squishy 12"... really anything squishy, as long as its 8" or more) constantly for a given amount of time. Start with 30 seconds; if that's too easy, feel free to increase your time. Again, several sets of 30.
One last drill we do is to put a block or a panel mat (nothing really above a foot and a half, maybe two feet) and practice doing jumps from the ground up on to it. 10 of whatever jumps you need. Be careful with this one though, because it forces you to travel forwards when you do your jumps (it's fine for the drill, but don't let it happen in your normal jumps), and depending on the jump may force you to move your legs strangely to avoid hitting the block/mat (ex: pike jumps).
One last general warning: stay focused while you're doing these. I've seen more than one gymnast roll an ankle or just catch a block with her foot and completely whipe out.
In terms of flexibility... what kind of jumps do you need more flexibility in? Split? Straddle? Pike?