Heater core problems
 

I have my dads '92 F-150 4.9L. The heater wasn't working so I took a look. There was sludge in the radiator so a flush was in order. Along with the flush I replaced all of the hoses (radiator and heater), and the thermostat. I still don't have a working heater. I pulled the heater hoses and flushed the core There was some color to the water but it soon ran clear, both ways. After the engine reached operating temperature I discovered that the inlet hose is too hot to hold while the outlet is just a little warm. any ideas?

If air gets trapped in the heater core sufficient coolant cannot circulate to provide good heat output. With the engine idling if you can back off the upper heater hose from the heater core to allow any air to escape, that is one of the ways to get the air out.
If it isn't a trapped air problem the heater core itself may be so plugged that you may need to replace it.

The inlet and outlet are side by side. I don't have an upper and lower. Which one?

In that case with the engine off just slightly pull back either hose and see if any air comes out.