Well I can't speak for how to make flour enchiladas, as enchiladas are made with corn down here as nature intended

I can say when I make soft tacos/fajitas and opt for flour, we wrap the flour tortillas in foil and bake in the oven for a bit first. Or if we're in a rush, wrap them in wet paper towels and microwave (but have found that this is very short lived heat, changes the texture for the worse, and does tend to dry out). Honestly, though, if the only flour tortillas you can get are the waxy kind you buy off the shelf at the grocery store, it's just hard to ever get them very tender. If you can find a local restaurant that makes them by hand, it's worth it (and cheap usually) to buy them from there. The results will be so much better, I promise.
Honestly, the only people I've ever met who made enchiladas with flour tortillas were from (or using recipes from) states north and east of the southern border states. The few times I've had to eat them this way (usually pot lucks), they were gooey/gluey on the bottom. Blarghhhh. I urge anyone who's never had them with corn to give it a try.
Can't say any tex-mex enchilada I've had was flour either (being as I'm actually IN Texas), though some chain places do use a thicker, larger white corn tortillas, such as Chuys.
Anyway, the way I was taught to make them was to very briefly fry the corn tortillas in oil to make it soft (but not crunchy), dip it in your sauce, then roll it around your filling. Put in a pan with some more sauce, top with cheese if you like. I use all kinds of fillings/toppings, but my favorite is a red or verde sauce. I finally perfected my red sauce. I'm not so hard-core that I cook down fresh tomatoes and grind my own dried peppers or anything, but it's a good mix of simple and tasty using tomato sauce, salt, quality chile powder "toasted" with oil to bring out the flavors, cumin, garlic, stock and a bit of cocoa powder for depth. Mmmmmm...getting hungry
I can say that the one of the things I miss about my ex-SIL is her family's cooking. They were all from Durango, MX, and her mother would hand make the most amazing corn tortillas. Of course, they mostly used these to eat cabrito, NOT enchiladas
