I have a string of down lights (5) in my kitchen that are controlled by three different switches (Two on/off switches and one dimmer). I want to add one more light to the end of the string that is connected to a dimmer. Going into the dimmer is two set of wires – One with a black and a white and one with a black, red and a white. I added a junction box where the new light will be to connect to the new light.
My question is which wires from the junction box need to be connected together to work the new light?

Is there a reason for trying to connect at the switch? You may or may not be able to do that depending on how things are wired.
Suggest you just run a cable from one of the existing light fixtures to where you want the new light.