Chad, sorry I hadn't seen your earlier message for some reason. I wasn't successful at melting iron in my sawed off cupola furnace with charcoal (not compressed). Even after adding an extension. Charcoal works well for melting aluminum.
oldgoaly, since Ironman has suggested coke itself as a binder I wonder if your petroleum coke could work that way with charcoal, or with itself? The catch is that in general to fuse coke you need high temps and lots of heat, which kind of defeats the purpose of a fuel, particularly a purchased one! Can it be compressed at low temperature?
But maybe if you used the flour as a low temp adhesive, and coke as a high temp adhesive for charcoal, or for itself, briquets could be made that stayed bound through the burning process.
Where do you get "petroleum coke"? Are you in UK, US or elsewhere?