To the best of my knowledge**, coconut flour does contain starch -- despite the fact that lots of people here are able to get away with eating it and nobody has
ever mentioned it failing the do-it-yourself starch test with iodine.
Although it sounds like not one of those people who can get away with eating coconut flour right now, after a couple years of successful dieting to let the gut recover, it might work fine. That is what I'm hoping for myself.
** I had pretty much the same experience as you with respect to stiffness after eating Bob's Red Mill brand, and after about 4 or 5 days was so noticeably stiffer that my physical therapist told me "whatever you're experimenting with this week, cut it out". If you look at the nutrition label on Bob's Red Mill brand, it implies there is 1g of starch per tablespoon of flour (net carbs - fiber - sugar). So I emailed Tropical Traditions hoping they had a lower-starch coconut flour, and their response was that if I could only tolerate trace amounts of starch then try coconut cream instead -- their flour had a bit more starch than Bob's Red Mill. Coconut oil was better still, totally starch-free, but it's pretty hard to eat by itself. Neither one helps in the area of baked goods

P.S. I hope this post doesn't offend anybody who is super confident of their home iodine tests, but it seems reasonable to me that the commercial tests paid for by the flour manufacturers might be more accurate. Also here is an alternative theory as to why coconut flour is good for many people despite being low-starch rather than starch-free: like the celery root that Alinus eats, it probably contains beneficial components that often (but not always) out-weigh the effects of the starch.