Disconnect the heater hoses at the split, on the inlet side, (passenger side) and at the inlet tube at the water pump. (drivers side.) Have something handy to stuff in the hole of the inlet tube, and use a pair of needlenose vice grips, or something similar, to crimp off the waterpump side of the heater hose on the passenger side. (keeps you from losing coolant out of the engine, or, at least, limits the loss.......)

Then, just flow water thru the two loose hoses that go to the heater core. Run it both directions, a couple times. If crap comes out, keep going until you get clean water out of it, in both directions. When you are done doing that, just hook the hoses back up, run the engine with the radiator cap off, and burp the cooling system again. Top it off, and see how well your heat works now.