How do you unclog the heater core in a ford edge

May be thermostat or clogged heater core. The third link uses garden hose to flush heater core.
How To Unclog a Heater Core - EricTheCarGuy - YouTube

HOW TO KNOW IF HEATER CORE IS CLOGGED UP, PLUGGED UP - YouTube

A way to unplug heater core
This Is How To Unclog Your Heater Core For Free In Minutes At Home - YouTube

look under the hood to see where the lines go into the firewall, the heater core is directly behind those lines in the cab.

Check that the cooling system is fully serviced (near full mark in coolant reservoir). With engine warmed up, feel (carefully) both heater hoses where they go into the firewall. If both are hot, there is water circulating through the heater core - possibly problem with blend door actuator. If only one hose, or neither hose is hot, you may have a blockage in the heater core. This usually means replacing the heater core, but you may be able to flush it. See this YouTube video: https://www.youtube.com/watch?v=M9SIafVsqyc

to by pass a heater core just connect the two hoses to the heater core together with a connector and hose clamps.

SEE HOW TO REPLACE YOUR HEATER CORE HERE. GET 25 GIFT CARD FOR EVERY 100 SPENT ON ONLINE SHIP TO HOME ORDERS

If the thermostat is not opening (coolant circulating) and getting coolant through the inlet hose of the heater core you will not get any heat. If the thermostat is working then the heater core is clogged. Some folks take the heater inlet and outlet hose off and flush each end with a garden hose, got to give it enough pressure to unclog the core.

The new cores are really thin and rather cheap,it's best to just replace it.
Messing around with flush and the like might get it to unclog a little but not like a new one.

No easy way. You can try backflushing the heater. Might try disconnecting both heater hoses and useing a garden hose to attempt to flush water backward throught the core.

replace heater core and yes its a pain