A lot of plant fiber is just extracted by pealing it off the plant skin in strips. Those strips are then woven into a design, to harden it you can use the sap of another plant (note: old tanners use brains and pee to tan hides). So, if I just created a number of two by two squares and then linked them together, I could have a very flexable outfit. China once had armor of folded paper that was laminated, used by the common troops, it only lasted for so many battles but it was good enough to stop one to five attacks from arrows and swords.
You also have bone - wear the dead! There is a way, soaking them in something that then allows them to be shaped, it then hardens them. Add to this another laminate and you could have a good armor base.
As far as Chitin goes, hollow out and wear. You can also add a laminate to it. One of those "how to make it in the wild" shows have the guy strip the skin from a dead seal and put it on like a wet suit!

Same theory applies with Chitin, not too flexable but can be done. What I see being done is the Chitin makes the plates of the armor. Gaint spider and cave crabs can be the supply source and also a food source.