I've done a fair bit of research into period crime, which overlaps with period gaming quite a bit. The following is a footnote from my edited version of The Book of Coney-catching by Robert Greene which should go some way towards explaining the various types of false dice. The term is taken from the legal jargon escheat, property which is reserved for a specific lord's use.
Flats are dice which are 'flattened', longer on one side than the others.
The two kinds of dice are swapped in and out by sleight of hand to suit the Cheater's needs. Dice with some of the sides scooped out slightly, so as to make them less likely to roll those numbers. Hope this helps.