I’m looking for a full frame DSLR camera that can take 3 shots at full resolution in less than 4ms (total), with a USB 3.0+ interface. Ideally, a Nikon. Any leads would be much appreciated.
3 full photos in only 4ms is well outside the realm of current mainstream DSLR camera specifications as of 2019.
Your options will be limited to fairly advanced scientific grade gear, or using multiple cameras set up in a chain-firing method.
You will likely need to seek rotary mirror/prism setups if you require sighting through a single lens.
I have worked with a custom rig to connect off the shelf modern digital cameras to a rotary prism, where all the cameras were set with a 'long' shutter speed that fired at once, and the actual exposure was then controlled by the lens and prism assembly, but I would have to go digging to see if anyone actually sells such a device.