There are so many unknowns here... is it going to be scrappy, or a fixed set of fabrics? How many fabrics if a set? How wide are the strips going to be? How wide are the braids going to be? Are there separator strips, and if so how wide and what are they going to be made of? How big is king size? Is there going to be a border around the braid section? It's almost impossible to answer the original question with anything meaningful.
In general, say that your king size quilt is going to be 110x110. That's 12,100 square inches, or almost 8 1/2 yards of 40" wide fabric. But you have to account for seams. If your strips are going to be 2" wide finished (2.5" wide unfinished) and 6" long finished (6.5" unfinished) and if you assume that most of your quilt will be made up of the strips, that means you're using 2.5"x6.5"= 16.25 square inches of fabric to cover 2"x6"=12 square inches of your quilt surface, so you need to increase the 8.5 yards up by a factor of 16.25/12. (8.5 * 16.25/12 = 11.5 yards).
So my guess would be that you'll need around 11.5 yards of fabric, give or take, with all the unknowns factoring in to make it more or less. If you're not going scrappy you will probably need more total, since there will probably be some fabric wasted on each cut.
Not much help, huh?