I've read about using buttons made just of linen thread on linen shirts. Apparently they're the only type of button that could survive the frequent and rigorous washings of the period. However, I couldn't find any resource online that told me how to make them. There are plenty of instructions on making Dorset buttons, but I didn't want to have the brass ring inside the button. Based on one of the very few pictures I could find of thread buttons, I made some of my own. If anyone sees something I've done wrong, please let me know, but as far as I can tell this works just fine.
Take a long length of heavy linen thread (I used a 16/2 double-strand thread) and wrap the end a whole bunch of times around an awl/bodkin. The tapered bodkin I have is nice because I can slide the ring up a little bit to loosen the tension and get the needle underneath. Depending on where on the bodkin you start you'll have a wider or narrower inner hole to the button, and how many times you wrap the thread will determine how thick the button is. I tried a few times to get one that I liked.
Make buttonhole stitches all the way around the ring of thread. Try to get the stitches close together, and pull them tight or else your button will be floppy, and won't fit easily through buttonholes.
If you'd like, you can just tie off the end of the thread when you've finished, and simply sew the button on without a shank. I chose to make a shank just by sewing across to the opposite side with the tail of my thread and tying it there instead. That gives you something to sew onto.
Here's a picture of my finished collar with three thread buttons. They won't really show when you're wearing a neck stock or cravat.