A 16 point rose is 8 pieces each of two contrasting colors.  (And 360/16 = 22.5 degree angles)

You start with a whole lot of straight lines.  In this case, I'm aiming for a 5-6" compass rose.    So I'm cutting a lot of ~3inch tall pieces.  You can size how wide the pieces are by lining up the template on top of a 3" tall strip of veneer, and then cutting a little wider, to give yourself a some breathing room.  Each of these 3 pieces will eventually yield 2 triangles.
 

Now, I strongly recommend you cut a ton of extra triangles.  First because this is paper thin veneer, and well, feces happens.   Second, its easy to batch out a bunch of these at the same time.  Worst case, you make some mistakes, and you keep and inlay the best result.  Best case, you have a nice spare pile of compass roses to spruce up future projects.

We're almost ready to cut... But first, we need a really straight reference surface.  So we joint BOTH sides of each of the pieces.  This is accomplished with a few swipes down our veneer jointer.  (Be sure to vary where you go on the surface and don't use up all your sandpaper in one spot)

If you hold up your edge and jointer and don't see any light, you'll be fine.  Hard to see but I have a raking light behind the jointer to help me look for gaps.   Once both sides have been jointed straight, you can move on to cutting.

This part is where you need to take it slow.  Fast is going to wreck pieces.  Hone your marking knife if it begins to dull.  You can see my strop in some of the photos to refresh that edge.

Line up your template with the top corner of the veneer carefully.  Make sure the veneer and the template are firmly against your cutting board side.  Then, press down on the template to make sure your veneer doesn't shift around on you.  Since your marking knife is single-sided, it will want to pull the veneer out.  You don't want that.  (You don't see me holding the template in this picture because I needed one hand for the phone photo, as a pathetic amateur.  I'll have to get a nice GoPro someday!)

Now, don't try and cut through in one pass.  That way lies madness.  First, just score the cut like you're laying out a line.  Then keep going over the line with light passes until you make it all the way through.  One softer veneer, you'll be through in just 2-3 passes.  On harder, you could be there a while.  Don't forget to strop your knife when things start to take longer than usual.   If I batch out 3-4 roses in one whack, I'll usually lose a piece of veneer or two here from just not apply pressure to keep things in place, or letting the knife slip or just trying to rush to fast and power through.   Don't be me!

Pretty soon, you have a Pile of Triangles.   Now take all those offcut triangles, flip them over, and repeat the process until you run out of pieces.