Any clinical research - long Covid + flu shot

I think you are doing the right thing to seek good information while taking that decision seriously. In the final analysis, only you can make the decision.
It comes down to weighing risks, some of which are unpublished individual reported experiences.
One thing I can suggest you factor into your decision is whether you are able to greatly minimize your risks of contacting the Flu thru sequestering, very solid + consistent medical grade protective equipment when in an environment for exposure. This includes the public health practices of those you live with.
You will find every possible opinion when you ask any group because we're in new immunological territory today.
And we are all somewhat biologically different under current COVID circumstances.
I have made my 2022 choice based on my experience of LAST YEAR'S vaccine. Vaccines change somewhat annually. I had an undesirable outcome in context of MY medical status at the time, one year ago.
I live in a very saturated infectious area currently and I still have not wavered in my choice. I am wiling to take the risk of infection, which would be extremely serious. My decision is purely my own. I would not make any recommendations for anyone else. I believe vaccines in general save many lives. I know there are undesirable effects for some. Outcomes are not predictable in complicated biologies of a subset of people.
Looking forward to reading posted studies.
Wishing you a good recovery from your current challenges.

I haven't seen any research, but from my experience with my own long covid and covid boosters, I was advised not to receive anymore covid boosters. However, my doctors did encourage getting the flu shot. I was nervous since everything I do sets me back into relapse. I finally did it and had no adverse reaction other than a sore arm. I am so glad I did it, since the flu is everywhere, and all the people I know that have it, did not get the flu shot. Take if for what it is, and only you can make that decision.

I can’t give you research statistics. Talk to your docs about what kind of flu shot is advised. I was told to get the one in the arm. I did and only had a sore arm. The nasal mist is a live virus and thus can affect your body differently.

My Internist and I have talked about another booster shot and the flu shot.
My doctors advice was to not get them. Due to my immune system dealing with long Covid.
We just don’t know what will happen if I do get the shots.
I’ve been stuck on the couch not able to do much at all. We can’t afford me becoming worse!!