Not Well...
I can't think of a PoD by which Brown and his group can possibly put together a big enough, sufficiently prepared group to handle what will surely come down their collective throats. There will be hundreds, and if necessary, thousands, of militia with comparable small arms and with trained leadership. Regular army units (led by Robert E. Lee OTL!) and military academy cadets will join in, and some of them will bring artillery. The northern states will not help the rebellion and may send their own militia. The only difference will be the body count.
Unlike with, say, Haiti, slave rebellions on the North American continent never succeeded. There were always more whites than slaves, and there were no natural barriers behind which the rebels could consolidate.