Why does only the hot water in tub faucet flows out in slow trickle but the cold comes out fine?

Is it a central water heater or a local point of use water heater?

With the centralized system:

• Hot water pipes are more susceptible to corrosion then cold water pipes, the hot water accelerates the build up of rust. If you have galvanized piping, that can be a major source of slow water.
• The hot water heater may also have problems which reduce the rate that water can get into the tank and from there on into the piping system. You might insure that the valves on the hot water heater and along the flow path are all fully opened.

With a point of use system, it may be that there is a control valve that won't allow the water to flow unless it is a certain temperature. If it is taking longer to heat the water, it could slow down the flow considerably.

When the hot side pressure is bad in all of the house it is going to be a problem with the hot water heater outlet usually. If it is just bad at one location especially when it is the shower and your shower is a single handle unit, it is the cartridge in the valve body. It is a very common problem with Moen valves as well. Simply replace cartridge by removing trim then cartridge and install new one. They should carry your part at Home Depot. You will be back in business.

If it is all over the house try replacing the hot side nipple and supply line coming out of heater,that will usually take care of it. If not it could be build up in piping and you might need a repipe.

http://aw-sons.com/slow-hot-water-flow-in-shower/