I use the same 100% Polyester Gutterman brand thread that Barb uses. It is thin so hides well is very strong and is available in a huge range of colors.
I have seen kilts sewn with a thicker thread. I have seen kilts sewn with Cotton thread. I have seen kilts sewn with Silimide thread. I have tried Silimide thread and it works very well but is not available in a wide enough color range for many Tartans and is much more expensive.
For my internal pad stitching I use Coats and Clark brand extra strong upholstery thread.
I do not use thick thread for pleat stitching and never use cotton thread for kilts.