gherkin, first may I ask Why a paint brush? are you looking for a different look ? and Unsmooth finish?
The only time I have seen this done is a farmer painting his tractors this way and looked rather nasty.
If you added alot of Flatening agent into the paint it should knock the shine off , but not for sure using a brush. It might also look shiny in some spots and flat in others because of the thickness of putting it on with a brush. And you would have to catylize it and then it may not even Kick ( dry) because it hasent been atomized by air.

And I might point out that it might take 3 times more paint to do it this way as it wont go as far brushing it on , as to spraying it on.

type of brush? depends on how rough you want the surface to look i guess , as any brush you use will leave brush hair marks and plus you will have alot of bristles left in the finish too.

Good luck , SprayTech