Initially, I didn't plan to make any blog posts for this project because I didn't know if it would work out or crash and burn (still don't).
But since this was something new for me, I figured I'd post anyway and maybe I'd get some helpful tips from the community along the way.  (Even if it's in the form of, "what you should have done was....")  😁

I used veneers that I had on hand:  dyed poplar for the blue, red, yellow, orange (unfortunately, no green), fumed oak for the "lead" lines, and bleached obeche for the white field.

My strategy is to split the panel into a number of smaller modules that will be assembled into the whole after they're completed.  I'll use blue tape on the underside to hold everything together temporarily.  Once the full panel is complete, I'll apply veneer tape to all the seams on the top, remove the blue tape, and vacuum press the veneer to a substrate.  I think it will work as long as I'm extremely careful when removing the blue tape.

With a little research online for techniques on cutting uniform veneer strips, I found this technique show up in a couple different forms.  Essentially, it's a cutting mat with a fixed fence at one edge and a straightedge clamped a uniform distance away from the fence.  The straightedge is elevated off the mat by the thickness of the veneer (or slightly higher) so that the veneer section will slide underneath freely.

I grabbed a piece of hickory with a jointed edge for the fence and a square-edged aluminum yardstick for the straightedge.  With a dedicated piece of scrap 3/4" plywood for a spacer, I clamped the straightedge in place and started cutting.  Sometime after I took these pictures, I unclamped the fence and put a deep rabbet on the top of the fence edge.  This was needed when cutting narrow strips to keep the fence from interfering with the cutting tool.

I experimented with a utility knife and rotary cutting tool.  In most cases, the rotary cutting tool worked best.  I went online and ordered a couple more cutting tools - a better quality utility knife and a circle cutter.

I cut a small supply of squares and strips and got started on first module - the first couple inches along the top of the panel.  I inverted some blue tape and taped down the ends to hold it in place on a scrap of melamine.  I understand contact paper would work too, but I didn't have any.  I laid the first border strip along the edge of the tape and started building the pattern above it.

That's the first section of the top, minus the vertical side strips which will be added as one of the last steps.  Next was the single stripe of black/white squares running down the center from the top, which I didn't photograph going together.  Its final length defines the position of the flag and cluster of squares beneath the circles.  I built that module next.