I would expect that there are analog sewing thread.
I would expect that there are analog sewing threads, but you would have to determine (or get some one else to) what the cross match is for a particular thread. Most common sewing thread is cotton, which would most likely pose problems with: longevity, thread size versus weight and potentially how the thread is twisted/wrapped preventing it from laying flat.
Most common fly tying thread is nylon, and it is waxed.
Many fly tying components are: a very specific type of a common item and/or subject to some post manufacturer treatment. Of course, many are just common items that some company has taken the time and effort to order the right colors/sizes and re-package them.
With some effort and time, you most likely could save yourself some small amount of money (presuming you do not commercially tie). You have to weigh the effort and time versus the potential to save, and you have to be honest about the savings by including the cost of driving to various craft and sewing stores.
I have looked at sewing and craft stores, while being there with my wife. I bought few matches (mostly yarns and chenilles), but I mostly did it to kill time.