How would you even tell?
I've had the subjective experience of feeling unable to complete thoughts I would like to think through, mostly as a consequence of post-traumatic stress.
It most often manifests as something like "A, therefore B, therefore C, therefore oh look a bird!" repeating over and over, along with an intuitive feeling that all the aborted chains are pointing roughly in the same direction. It sometimes manifests as "A, therefore NOT B" in cases where if I abstract over the particulars sufficiently it's obvious that A -> B, and I can't figure out why on earth I concluded NOT B in any particular instance. (Often followed by "A, therefore NOT B" in the particular instance again.)
I typically describe both of those experiences as my mind skittering off the surface of a thought rather than engaging with it, though the actual experience isn't kinesthetic like that at all.
That said, I don't experience any of that as being at all related to the sensation of "free will" the OP is talking about.
This points at the question of how much free will do people who believe in free will think they have? There might be a difference between free will and omnipotence about one's thoughts and decisions.
Given the spike in free-will debates on LW recently (blame Scott Aaronson), and the usual potentially answerable meta-question "Why do we think we have free will?", I am intrigued by a sub-question, "what would it feel like to have/not have free will?". The positive version of this question is not very interesting, almost everyone feels they have free will most all the time. The negative version is more interesting and I expect the answers to be more diverse. Here are a few off the top of my head, not necessarily mutually exclusive:
Epistemic:
Psychological:
Physical:
For me personally some of these are close to the feeling of "no free will" than others, but I am not sure if any single one crosses the boundary.
I am sure that there are different takes on the answers and on how to categorize them. I think it would be useful to collect some perspectives and maybe have a poll or several after.