How to deal with signal not equally spaced in time when performing FFT?
It sounds like you are dealing with 'missing' data. Usually in cases like this, you can perform a simple polynomial regression on your data first, and then FFT. 

In this way, you will fill in the gaps of the missing data based on the model polynomial you pick. Once you do that, you can perform an FFT. I would try this method first, before considering anything more involved. If you put an image of your data as well with the missing samples, that would go a long way.