I am trying to fit a 7" flex duct between some floor joists and it would fit better without the insulation. Can I remove the insuluation and just use the plastic part?
Technically I suppose you could remove the insulation around flex. Why would you want to though? I understand that it fits tight through there but in my installation of commercial duct work (on the side) we have just compressed the insulation. It is after all flexible. One thing that insulation around duct work does is prevent condensation on your ducts when you run the air conditioning in the summer. You may think no big deal but that slight bit of moisture and a couple of drops can start other issues. It's good to keep your ducts insulated. I would say either pipe it through the (and insulate the pipe) joists and put flex on after that or just squish the flex with the understanding that it may affect the airflow to that room (depending on the squish factor)
The insulation does give a measure of puncture protection to the inner duct. It is a thin and somewhat brittle plastic. If possible, I would remove just enough insulation (on the joist sides), to make placement possible.