pure plain dyneema is too slippery to use for a halyard for the most part. However, you could do a blended single braid like apex (but not sure you can get it in 3/16). What came with my boat- and what you probably have is the 3/16 spyder line which is actually really good stuff.
I had the problem with lots of kinking in the past on a previous boat but most of it can be solved by making sure you run all the twists out of the halyard before you set it up on the baot. If you coil it you need to unwind it all the way to the ends- making several passes. Usually that will get rid of the twists and it shouldn't kink. I tapered both ends of my halyard (the snuffer end to protect the sail/snuffer hoop- although that is probably unecessary with the aluminum hoop) and the halyard end to "save weight" (HA!!! nope.. I like splicing/tapering and I was bored one evening). Tapering probably won't solve the problem as much as making sure you unwind it.
If you want me to taper you let me know.. all it will cost you is shipping as I have nothing to do in Michigan right now. (same offer goes for any of my f16 compatriots, tapering, splicing, etc. not double braid eye splicing though.. ewww)