My 99 Blazer won't blow hot air. The Heater core

Assuming that you have the proper amount of coolent added, check where your heater hoses connect to the engine block for rust and corrossion, this is a common area to clog up, preventing coolent flow from circulating through your heater core. If ok, check for a thermostat that is stuck open. Sounds to me your "backflushing" has moved a plug of corrossion and rust deeper into the engine, and over a short time, it has moved back up to reclog your heater port.

check to see if there is plenty of antifreeze in radiator , may have a air bubble in system .

heater core plugged. remove heater hoses, use tap water to flush out core..

Sounds like a restricted heater core. Remove the hoses and back-flush the heater core system with a water hose. You may want to do a complete cooling system flush while you're at it.

If you can't flush the heater core clean with a water hose, it may be time to replace.

if the fan blower is working then it must be the heater valve inline with the heater hoses. Or the selector on the dash has broken and is not connected at the back. You have tried everything else. You were correct in what you wrote above and have tried so far

Is the fan turning on? I assume so.. when you change the hot/cold selector do you hear the flaps inguage? could be the linkage there. Otherwise, check your coolant level - make sure your heater core isn't plugged (let engine heat up, then see if the heather both heater hoses going into the firewall are warm). If one is colder than the other, flush the heater core.

Let vehicle worm up grap bolth the heater hoses that are attached to the heater core if therew bolth not hot then there is now flow through the heater core and its likely pluged you will have to flush it out by forceing water through it back and forth from one side to the other this heater core is not easy to change i owen to same vehicle

You need engine heat, circular, and a blower to get heat. You've already done the first steps of making sure you have enough fluid, etc.
Circulation - water pump - not likely because when they fail they usually bind up or leak really badly.
Heater core - would be my next guess. If this is blocked you won't get any hot water to blow air through. The heater core goes through the firewall. If you can get to the hose connections, disconnect them and see if you can flush any water through the core. Most likely you will have to replace it.

You likely have a restriction in the heater coolant hose circuit - perhaps a coolant control valve not fully opening, or a kinked hose.
Insufficient coolant volume is flowing to keep the heater core hot.
Try back flushing the heater core system with a garden hose to check flow.

your core could be clogged. you can flush it by removing both heater hoses coming from firewall and spaing the garden hose in one and then switching to the other until clean.

repair shops will not flush core when flushing coolant unless you ask them to.