What are the rules nowadays on flying non-spillable batteries?
Here is the information provided on the TSA website:
http://www.tsa.gov/travelers/airtravel/assistant/batteries.shtm
They couldn’t possibly fly…they’re too heavy. 
Seriously, though, we wondered the same thing, and talked with our carrier several times with all the battery data on hand and got answers that ranged from a solid yes to a solid no. With that (no way we want to run into “solid no guy”), we contacted the folks from our supplier, found out how they ship, and shipped 2nd day to the hotel where we’re staying. I hope they know who’s coming (FIRST) so they aren’t concerned when odd things start showing up on their doorstep!
I believe that you’re supposed to ship them, not fly them. In the past few years, since we’re from Atlanta, we’ve had teams from Israel and the Philippines ship their batteries to us, and we just gave them back at Championships.
If your team needs to do the same, let me know and we can work something out!
Not allowed 
We’ve flown batteries across the Atlantic and back, one even in carry-on, but IIRC they were very specific batteries, not just any batteries.
What’s your basis for saying this?
MK sealed lead acid batteries meet specific requirements for commercial air transportation (ICAO special provision A67, packing instruction 806). The TSA only specifically excludes spillable batteries (except in wheelchairs). Did a carrier deny your request to transport properly packaged batteries in checked luggage?
You have more reliable sources than I do. I just remember asking “why not carry on a few batteries?” once and being told that it wasn’t okay, teams from other countries always got stuck without batteries because of it, etc.
we shipped the robot with the batteries. that’s the solution although it cost money.
There seems to be a lot of conflicting information out there from airlines, TSA, etc. I couldn’t get any solid answer. TSA says it’s under FAA’s rules, but the only document I found was regarding wheelchairs specifically (in which they’re allowed if disconnected, but on some airlines they don’t need to be disconnected). I couldn’t find anything specifically prohibiting it, but I always worry that if you show up with something that’s not a standard traveling item, they seem to jump to conclusions as to what it is. In 2008, we flew them all over the place without much issue… But in Hawaii, they stopped our luggage after about half of them went through, and had to take a half hour to call someone to figure out the rules. What seemed to cause them concern is they were in a box that originally was for a vacuum cleaner. Anyway, now with fees to check items, I think I’ll just send them to the hotel or something.
The last time I went to the Championship we 2nd day shipped a large box of batteries to our hotel. When we went to pick them up, the guy at the desk said, “You guys can go grab it from the back, I’m not carrying it around anymore! What’s in it besides the batteries, a big chunk of lead?!”
To summarize our 11-year experience trying to fly non-spillable batteries into the US, you can do it, by the rules, but the airlines personnel won’t allow you to. 
Yes, you can argue and sometimes persuade them, but it’s just not worth it when your flight leaves in half an hour. US airports already had a fair share of our batteries left behind, so we simply gave up. For quite some time now FIRST has provided international teams with loaner batteries without prior arrangements.
Probably the best advice is to ship/drive them to Atlanta.
We have flown them but the TSA gave us a lot of grief for it. I suggest shipping them if you still can.
We’ve had the same experience even when we carried all of the documentation with us. We’ve decided it’s not worth the effort anymore and either ship batteries in the crate or ship them to our hotel.