Basic question:) What brush should I use to repaint a file cabinet.

A sponge roller would work best. It won't leave brush strokes or shed bristles.

I would use a 6" foam roller myself.

What kind of paint are you using? I would use a good quality foam applicator rather than a brush.

I would try spray paint.

Use a fine roller

I've painted metal file cabinets with spray paint for metal by Rustoleum.

I wouldn't use a brush. For a file cabinet you want a near perfect finish. Spray paint applied in several very light coats should work.

Ditto on the foam roller. They make even coating easy and leave a very nice texture. Finish roll in one direction. A metal cabinet should be coated in oil based paint to avoid rust.