And if you think about it, a flap on a delta wing would actually be an elevator, so there's a problem. Hardly any deltas have high lift device, the only ones I can think of is the Mirage 2000 which has LE devices acting against drooping elevons, and the Typhoon which has canards which obviously have some longitudinal contol function. The M2000's I think (although I'm willing to be corrected) is largely automatic as a function of the fly by wire trickery.