When you depress the air presure butoon on the kohler whirpool tub a clicking sound is heard but the motor does not run. There nis powewr to the receptacle that the pump/motor is connected to.

Your problem is most likely NOT the air button but the switch in the motor.
Air Switch Repair
It sounds like you have a bad air switch located in your motor.
The air switch is what the air hose connects to on the back of the motor or on the box on top of the motor. The other end of the air hose is connected to the air button on the lip of the tub.
This is a latching air switch and when you push the air button it latches to send power to the motor. When the air button is pushed again it opens the latch in the air switch and stops power going to the motor shutting it off.

Rod
US Parts Center

If your air blower does not run for more than about 3 minutes then you may have a bad motor.
Once it shuts down it should come back on in about 10 minutes after it cools down.
Every motor has a thermal protection built into it to prevent the motor from burning up.
If this is the situation then you will need a new motor.

Rod
US Parts Center

Air Switch Repair
It sounds like you have a bad air switch located in your motor.
The air switch is what the air hose connects to on the back of the motor or on the box on top of the motor. The other end of the air hose is connected to the air button on the lip of the tub.
This is a latching air switch and when you push the air button it latches to send power to the motor. When the air button is pushed again it opens the latch in the air switch and stops power going to the motor shutting it off.

US Parts Center

Bath Spa Replacement Parts Hot Tub Bath Parts Accessories US Parts...

There are Air Switches (at the motor or control box) and Air buttons (on the spa/bath side). The vinyl tube between them is the only other component to the 'switching' on/off a hole in the tube may cause this problem.
The air switch has a diaphragm which is activated by the air in the tube when the button is pressed. If the air pressure is not sufficient the switch will not operate.
As you've replaced your Air button, you might want to change the tubing and either adjust the Air Switch or replace it. The switch only needs 1-5psi to activate so the pressure from you blowing into the tube can damage the diaphragm in the switch.

This is sounding like a relay not working on the circuit board inside the control box. You will want to have a Kohler service center send someone out to have it checked. You most likely need a new control box.

Check for an air switch at your local hot tub store

take the old one in so they can match it up to a new one

Most of the control buttons on a tub are not electrical. These buttons are connected to an air line that runs to the motor. Sometimes an aggressive button push can literally blow the air line right off of the bottom of the button.
This problem is as easy to fix as it sounds. Find the loose air line and push it back onto the button. You will need to open up your access panel. Bring a flashlight.
Be sure to check the connection at the motor too. Good luck

judging by the description i would say more likely the coupler
its a three peice part that sits between the mototr and transmission, kinda like a clutch,
anyway it is easily repaired
and available on appliancepartspro.com
type in your model number.....
look for motor coupler

Here is the manual for the tub. The switch is an air switch with tube. You have to make sure the tube has no holes in it or replace it if you can. look on the manual it will help you out.
http://www.us.kohler.com/onlinecatalog/pdf/1010564_5.pdf

This is a problem common to all whirlpool/air jet style tubs. The pumps become air locked due to the water evaporating from lack of use. All tubs need, and have, SOME means of priming the pump, this is most likely what the problem was, originally, for you. This time in particular you found it to be electrical in nature but for future reference, for you and all who have these style of tubs, I am putting this out there. Some where on the tub, usually along the top edge of the tub is a vent knob that controls the amount of air that the pump is allowed to mix with the water for the jets, usually by closing this valve all the way (tub needs to be full of water of course) and running the pump for a minute or 2, you should be able to get the pump pumping water again, if not you may need to do something else with your particular set-up to get it purged of air, the pumps in jacuzzi tubs are designed to pump water, not air, so if the motor is running but you get no jet action, your most likely air locked and need to prime pump/purge air.