coolant flush

Expect a LOT of gunk if that's an 03 and it's never been flushed = not good. The traditional green antifreeze used in these trucks is typically only good for 2-3yrs/35k or so, 8yrs is a LONG time. Expect to be flushing for quite some time, make sure your heater blower is open.

When you refill, after the radiator's full and you're attempting to get all the air out, make sure your heater blower is on high.

Also....change your thermostat while you're at it.

Having the heater blower on has no effect on the heater core what so ever. What you should do is have it on hot so the heater core valve is open. I would drain everything and pull one heater core hose and run the garden hose through it. I would also remove the upper rad hose and do the same. During both steps just have the lower hose off to allow everything to drain. Now close everything and fill with plain water. Run the truck and bring it up to full temp. Shut it off give it a few mins to cool down and drain. When draining asses how clean or dirty the water it. If you want you can do it again and use a cleaning agent. If it looks fine fill with a 50/50 mix.