Not flipping, like the f word... lol
Actually flipping

I installed a new naze32 flight controller, rev6, and my quad is now flipping backwards. I've literally tried everything aside from testing individual motors and ESCs.

Any tips about how to test them individually??? Or alternatively, how to resolve the issue entirely?

I suggest double-checking that your ESC's are plugged into the correct ports on the FC, and/or that your propellors are mounted properly.
(I'm not suggesting they are not, but sometimes those are easy mistakes to make.)

I would also make sure the FC is installed correctly, ie: the arrow on the board faces the front..if not you have to offset it in Clean Flight.

Agree with what Scotty and Biggle said..

Also check you have the correct props installed on the motors...

And did you calibrate your ESCs and set your min_throttle and min_command correctly? When you say "flipping backwards" do you mean on takeoff? Because that sounds exactly like what would happen if your motors aren't all firing at the same time.

If you go into cleanflight motor testing and check the configeration of your motors then test 1 by 1 you will see for sure if they are in the correct order.( not forgetting to take off the props first!!)