Why does the hot water tap in my shower start out fast then slow down to a trickle?

If the hot water tap in your showers start out fast then slows down to a trickle, it sounds like you have a defective washer, that rubber disk within the faucet that helps stop the water from flowing when you turn off the tap.

Although the washers in both faucets can erode with time, the hot water washer is likely to go bad much more quickly.

What happens is that hot water expands the rubber washer, and then as the washer cools, it shrinks again. This constant change wears out the hot water washer faster than the one in your cold water faucet.

The deteriorating washer can produce a number of results, from leaky, dripping faucets to a high-pitched squeal when you turn on the water.

In your case, as the defective washer gets hot, it swells and partially blocks the water flow, reducing output to almost nothing.

In other words, replace it.