Baseball fan/very occasional player checking in.
A baseball slide is just a foot first slide on your legs, usually when you do it you're trying to catch the corner of 2nd or 3rd base (never 1st base, you can run straight through 1st base and not worry about being thrown out by running too far) while also trying to not get tagged out... Which doesn't matter in paintball, of course
Just go foot first with one leg, and slide on the side of your other leg, and when you stop you'll find the momentum means you can spring up on to your feet and be in a shooting position.
Beauty of it is that you also stay nice and low, which I assume (having never played any supair ever) is a good thing for trying to avoid getting shot.