Highland, a program developed by John August's team, converts scripts from PDF or Final Draft into their plain text markup language for screenplays, Fountain. I don't know exactly what that means, but I do know it it's the best solution I've found to get PDF screenplays onto my Kindle.
Once you drag the PDF into Highland, it will convert it into Fountain - recognizing all the screenplay elements. Export as a Fountain file, then save as plain text. From there, you can get the file onto your Kindle by e-mailing it to your Kindle address, upload using a program like Calibre, etc.
The file still won't look *exactly* like a screenplay on your Kindle. Everything will be left justified. But the line breaks will stay the same, character names will be capitalized... all in all, it will look like a screenplay. And the text will be scaled appropriately for the Kindle screen, rather than the micro text that comes from trying to display an entire PDF page at once.
Highland is now a public Beta, and definitely worth checking out. It's also worth keeping an eye on Fountain based development in general, which suggests deliverance from many of the square peg, round hole problems that arise with the traditional proprietary screenplay software.
UPDATE: John August referenced my post and challenged developers to create an even better way to get PDF scripts onto the Kindle.
The discussion which followed is interesting. Several advocate using Screenplain to save a Fountain file as HTML. I tried this myself and found that, while the Screenplain HTML looks great on my computer screen, once it hits the Kindle it's still got the usual quirks - everything left justified, etc.