[Jon Shank] “What frame rate did he likely SHOOT in to be able to both slow down and speed up?”
You can speed up from 24fps, you just can’t slow down as easily (not without using post interpolation work, such as the Twixtor plugin). I would assume mostly 48fps, perhaps in certain cases (I cannot remember the movie well enough to remember how slow the slow motion goes) as high as 120fps (the limit of the Alexa XT).
[Jon Shank] “Is this something I could do with a dslr? Say by shooting in 24 and then interpreting/conforming it to 26+ to make it sped up/choppy and down to 21-23 to make it slower?”
Yes for the latter and not really for the former. To get the quality of slow motion like you saw in Fury Road you would need to shoot at a bone fide higher frame rate. And that depends on what DSLR you’re shooting with. The A7S Mark II, for instance, will do 1080 at 120fps. The Panasonic GH4 will actually do 48fps in VFR mode (which means no sound capture on camera). The Canon EOS 7D Mark II will allow 1080 at 60fps, while the EOS 60D would only allow you 60p in 720.