I think you're correct that you need to start in the middle and work out. If you ignore the 4-piece corner triangles, the center of the block is a 9-patch with three types of units. The center is a 9-patch, the corners are HST, and the remaining units are rail fence.
When you make several of the complete blocks and lay them out, you'll effectively have two different 9-patch blocks alternating and on point. The other 9-patch will be plain squares with white in the center and on the corners, and the blue and red fabric in the remaining four spaces.
I would assemble the quilt with the two different 9-patch blocks, and use setting triangles on the ends of my rows. There are calculators and tutorials to tell you what size to make your setting triangles. If you want to do it exactly like it is drawn here, you can just make the 4-piece corner units with a square, two QSTs and one HST. Either way, you'll have to decide what size you want your block to be; I'd start in the middle again and make the measurements easy for the smallest units first.
Hope this helps,
Darren
P.S. I'd like to see this one going together; would you mind posting progress pics?