Ok, here's what I've got for that:
First, you should have a strong press to handstand. You don't have to be able to do it from straddle support (though that helps), you just need to be able to do it from a stand.
For strength (and you can work this process in parallel with the drills below), work the press handstand with your hands starting higher than your feet (ie hands on a panel mat, feet on the floor). As you get this, increase the height gradually, until eventually you're starting in a front support with your feet off the floor and pressing to handstand (parallel bar blocks are great for this).
Next, swing in support on either parallel bars or blocks. Do a 3-count, and on the third swing, instead of staying straight as you swing up in back, pop the hips up and straddle so your feet end up on the blocks behind your hands (the closer to the hands, the better). From here, press up to handstand, then swing down and repeat.
Once this is strong and consistent, do the same thing, but miss your feet; that is, as you swing up in back, straddle and pull your feet towards your hands, but press up without them actually touching the blocks.
Final step: put two blocks behind a single rail, such that they are parallel, close to the bar, and have a gap in between wide enough for you to swing your legs through. With this setup, the process is essentially the same as it was on the parallel bar blocks. Cast to a straddle stand on the blocks, then press to handstand, and when you get comfortable with that, you simply miss your feet and press all the way up. And voila!
Hopefully all of this makes sense; if not, let me know and I'll get some pictures or videos.