Insufficient amount of coolant. This forms air pockets which is the gushing sound you're hearing. This can typically be addressed by 'burping' your cooling system when you flush and clean it.

As for whether or not the flush process will also clean out the core, I'm not sure but I hope it does.

In terms of cleaning it out, you may also be able to connect your flush kit directly to the heater core hoses (bypassing the engine entirely) to focus the flush process on just the core.

Oh, I should add that I'm not a mechanic but I did stay at a Holiday Inn Express last night. <img src="/forums/images/graemlins/lol.gif" alt="" />