The Brompton kits are designed for 160mm rotors and IS mounts. Most brakes will fit, though large callipers like the TRP HY/RD will not fit on the back. With disc brakes, levers with large reservoirs can cause problems when folding – that’s why I normally use Magura or Hope XCR brakes, their compact reservoirs don’t have this problem.
At the back, the IS adaptor should have a rounded end to fit inside the curve of the frame – Shimano XTR ones are good, Tektro also make one, or if you have a square-ended one then you can just file off a bit – just make sure it fits flush to the inside face of the frame.
At the front, with 16″ wheels, the mudguard stay can interfere with some mechanical callipers like the Spyre – to avoid this, simply bend the stay a little bit so it sits on top of the head of the calliper mounting bolt.