I am trying to calculate the phase difference between two signals, a sine wave and a cosine wave, using GNU Radio. I am using the following block configuration:

The problem is that I am not getting the desired output in the time sink block. I just see a constant signal with amplitude of 0 not changing over time.
Is my block configuration to calculate the phase difference between the two signals right?

As documented in the official Block documentation,
(emphasis mine)
So, this isn't surprising - you're multiplying exp(j·something) with its own conjugate all the time, getting a constant exp(j·0) = 1, which has argument 0.
Try changing the initial phase of either of these!