Litte Cold Water Flow from Kenmore Heavy Duty 70 Series Washing Machine

Does anyone know what could be causing little cold water flow?

what do you mean by little cold fill. does it let water in when the machine is turned off or when you set it to hot water it lets cold water in.

Given there is some uncertainty about just what Desparate meant by that, let me just make a few statements...

Hot and Cold, two separate lines.

Usually, the Cold has better flow, that being because the Hot goes through the Tank and more lines to get to the Washer.

Do you have those little inline Filters in the supply lines? If so, you may need to clean them out. If you don't have them, you should buy a couple and install one in each line.

If you don't have them in the lines, that may be what is causing the slow flow to the cold. That being that there may be a piece of trash (a flake of calcium deposit) blocking the valve to some extent.

Occasionally, (annually maybe) one should remove the Cold and Hot Hoses, hook a Garden Hose up on each with the open end of the Garden Hose like outside somewhere.
Then open the Valve and let the water flow as fast as it can. Discharge/clean the line out like that.

That should remove any accumulated debris from the line, where the little Filters can handle the rest.

Now...
IF you have a piece of trash blocking the Cold Valve to some extent, the only way to get it out, is to remove the Valve, disassemble it, and clean it out.

As long as you were doing Cold, I'd do the Hot valve just for good measure too.

Have a good Day !
S.W.