Continuous flashing red light, no flames but the blower is working fine. What is the solution to this problem?

You have low flame sensor signal. Clean the flame sensor with fine sand paper or steel wool. Becareful around the ignitor if you have the new style Honeywell since they are fragile.

Cleaned the flame sensor and I am still getting the same blinking light and the problem remains the same..

Literature

http://www.nordyne.com/literature/778a.pdf

See page 30 of this install manual below. I gave you the easiest and cheapest cure as you will find listed on the service blink code section under continuous blink as you described.(false flame/low flame sensor signal)

Now you are going to get into the gas valve area of the unit. If the wiring is not loose when you wiggle it around and check it for tightness I suggest you contact a HVAC company to make the repair. It is not a simple job since the new valve will need to be installed correctly and adjusted to factory specs using a monometer and other tools of the trade. I also suggest you save a copy of these for your records on the computer. I am sure you will ned these service docs again.

See page 30

http://www.nordyne.com/Literature/708291b.pdf