I've done a wee bit of flat-top checkering. You need to use a spacer tool to get the lines all parallel, I have used both a 16 lpi and a 10 lpi spacer tool - I liked the 10 best for the flat top work.
No one makes a 10-lpi tool that I am aware of, BUT there are 20-lpi "skip-line" tools that are exactly what is needed! You can go ahead and use the standard tool, then lightly sand the diamond tips off. The standard tool makes a "V" bottom groove.
I am contemplating making a "flat bottom" tool such as Larry Potterfield makes in his video. the only round bar stock I have is 3/8" diameter, but that should work just fine.