to flush you stick a hosepipe is the highest point and make sure the pipe at the lowest point is disconnected, then when you turn the hose on water is forced through hopefully removing any blockages.
a blockage wouldnt explain how air keeps getting in there, if you bleed it till water comes out, and then air comes out next time, it means there is water getting lost, or more specifically water is getting replaced by air. so you need to know 2 things, where the water is going to and where the air is coming from. the only options are a leak or headgasket failure. if there was a blockage it wouldnt cause air to enter the cooling system.
i bet you're getting very fustrated by now, i know i would be, surely its worth while getting a pressure test done on the cooling system, thats the best way forward and it shouldnt cost much at all.