I can't comment on the other string types because I have only ever made the flemish style. But I taught myself to do a flemish twist string in an afternoon, its quite simple. The jig isn't necessary, it just helps to get the individual strands staggered so that they don't end all in one place, as this would make it so the string it wouldn't twist back into itself as well when forming the loops. I can whip one out in about fifteen minutes, and my jig only took about 30 minutes to make.
To do it without a jig, just get the strands together that you need, cut them to overall length (compensating for the length that will be lost in forming the loops), and then cut one strand 1/2 inch or maybe 3/4 inch back from the end, then cut another strand another 1/2 -3/4 inch back, and so on. Then you can continue on with forming the loops and stuff.
But the jig is really easy to build and use. It looks more complicated that it is. If you are going to make any number of strings I would recommend building and using the jig. Plus the flemish style strings look pretty snappy and don't require any serving to hold them together