What is the most compact way to make a flat six pointed star in LEGO?
Hexagonal symmetry and angles in 15, 30 and 60-degree proportions are scarce among LEGO elements.

I think the smallest single piece that approximates a six-pointed star is the basic flower:



I myself don't practice freelance brick modification, but someone with fewer scruples might easily trim one of these into a 6-pointed star shape. 

Another piece that has hexagonal symmetry is the old pulley wheel:



The holes are arranged at 60-degree intervals around the center. Putting two of these pulleys together and inserting half pins into the holes will give you 6 studs arranged at what could be the points of a 6-pointed star:



I added a 1x1 round plate to three of the studs to offset the gear shift handles. This construction is a little shaky, as the half pins will rotate. Not sure if it's compact enough for micro-scale - the star ends up about 2.5x2.5

You could get a 6-pointed star of about the same size using two triangular roadsigns:



These have clips on the back. Putting them face-to-face would give you a clip on the front of the star, and you'd have to find a way to hold it in place, but it would have the advantage of being fairly thin. The color options on these pieces are limited, though.