I want to utilize a push button starter switch instead of using the switch included with your kit. Can this be done and how do I do it?

As you don’t mention which kit you have, I will address this situation in broad based form. There are actually 2 different ways of making this connection depending on what you are trying to accomplish. Both are very easy to complete. Generally speaking, there are two connections on a push button ignition switch, “power in” and “power out”, and it doesn’t usually matter which is which. On any of our kits at the ignition switch connection, you will find the following wires: Red; Pink; Brown; and Purple.
The first connection possibility involves the push button starter only working when the ignition is turned to the “On” position. To accomplish this, splice or double a 12-gauge jumper wire off of the pink wire at the ignition switch connection and take that jumper wire over to one side of the push button switch. Next, take the red, brown, and pink wires and connect them to our supplied ignition switch just as the instructions dictate. Lastly, take the purple wire and connect it to the opposite side of the push button switch where you connected the pink wire earlier. The push button will remain “dead” until the ignition switch is activated to the “On” position. Once the ignition switch is turned on, there will be power at the push button. When the button is depressed, that power will transfer down the purple wire to the starter solenoid activating the starter and allowing the engine to start.
The second way to make the connection involves the push button starter being hot and able to be activated anytime the battery is connected. To accomplish this, splice or double a 12-gauge jumper wire off of the red wire at the ignition switch connection and take that jumper wire over to one side of the push button switch. Next, take the red, brown, and pink wires and connect them to our supplied ignition switch just as the instructions dictate. Lastly, take the purple wire and connect it to the opposite side of the push button switch where you connected the pink wire earlier. The push button will remain “hot” all of the time, and the push button will be able to be activated and crank the engine all the time. However, that car will not start until the ignition switch is activated to the “On” position. Once the ignition switch is turned on, there will be power at the coil and the car will fire upon the button being depressed.
Either way is acceptable. If you have a racecar or one that needs to have the valves adjusted quite frequently, the second scenario would be advantageous to you as the engine could be rotated without fear of it starting.