What kind of flats are you getting? If pinch flats, increase inflation pressure. If punctures through the tread, try a different flat resistant tire or even thorn strips. If sidewall cuts, I guess look for tough sidewalls, I've never gotten many of those.

One thing is, when your tires get worn, flats increase. If I start getting more flats without any good explanation, I replace tires.

I had Armadillos in 26", they were pretty good. I use Gatorskins now, they have been fine.