There isn't any Olivine on the flats but there is green sandstone, green sandstone forms when Anoxic marine zones have a lot of organic waste, this tells us that the flats where probably underwater at some points, but we also can find green sandstone on the hills of Minmus. Olivine in RL is found in Earth's upper mantel, this supports the idea of Minmus having an active inside which could've created a magnetic field which could've allowed Minmus to have an atmosphere the green sandstone also shows us that Minmus had life possibly.
Ksp 2's Idea of it being cooled rock could also be right the Green sandstone and the Olivine could've been from Kerbin and the flats could be Marina's.