I know that in the sailing world it didn't take long for sailmakers to discover that kevlar did not like the over and under that was typical of woven cloth. The fibers quickly broke down. They found they could laminate tapes made of linear fibers to a mylar sustrate. The Kevlar was much happier in that arrangement.
When it came to cord, the solution was to mix Kevlar with other fibers so as to separate them from each other. This was done first with polyester and then with Spectra. This mixed type was quite successful. It was extremely strong and low stretch (good in sailing, bad in climbing), durable, and could be spliced. The other strategy was to arrange them in a bundle of parallel fibers (difficult to splice).
I still have a pair of 60 ft 1/4 inch spinnaker sheets that are made of this mixed material. They are rated at 3,600 lbs and I've used them on boats up to 37 ft as light air sheets. They are murder on the hands when the wind gets up. Just put lots of wraps on the winch.