I've made a bunch of my own chutes.
I have used Kevlar thread, but in my experience it's unnecessary overkill, and regular consumer-grade sewing machines don't like it. The thread tends to bind up and stick in the machine, due to it being stiff and coarse compared to "normal" thread. On the other hand, I've also used regular old standard sewing thread which always worked perfectly fine....easy to work with, cheap, readily available, sews just fine, and I've never had any actual problems in use/flight with it.
The suggestion for using 1.1 calendered ripstop is a good one. All my best chutes (by far) were made with this material. It's wicked light, packs tiny, opens easily in use, and performs great. That said, it IS kinda tricky to sew - mainly due to it being so slick. In sewing, it's very slippery and extra care is needed running it through your machine. I've found good deals on E(vil)bay for the material.
s6