I have a customer that is interested in using the below voltage acceleration model and I am struggling a bit with how best to enter this into the custom relationship dialog in the launch window. This is from a JEDEC standard for "Early Life Failure Rate Calculation Procedure for Semiconductor Components". Any input would be appreciated. Thank you!

The easiest way is to create a new column and enter a formula. You define the parameters and then build the formula using the parameters and data columns. If you are not familiar with this activity, then check the JMP documentation. The chapter for the Nonlinear platform under Specialized Modeling has a section on custom models. It is exactly the same thing.
If you get stuck, holler!
WAIT!
The feature in Fit Life by X is for a TRANSFORMATION. You want to look at another platform, Degradation, in order to model accelerated life test data. But what I said above about the way to define this model remains true.