Not clear where it is slow. If it is in the fill then there is a filter at the point the cold feed is connected to the washer. Disconnect it at the washer and check. If it looks OK take the opportunity to check that there is ample pressure of water by putting the end of the hose in a bucket and turning on the supply. Does not sound a difficult problem to diagnose but is it some other symptom?

Of course turn off the water supply at the isolating valve before disconnecting.