Haunters rarely call them flats... we almost always refer to them as WALLS or WALL PANELS.
A properly constructed, muslin-skinned, theatrical flat (with keystones and corner blocks) is quite sturdy and would probably work for 70% of your walls.
I've used them in the past and they work fine.
Just be sure to have a few extras on hand, in case of overzealous customers.
The walls in your scare zones really need to be skinned with plywood, of course.
With my 2004 haunt, I used metal brackets to attach the walls to one another, and then braced across the top with 1x3s.
The top bracing turns the walls into one big unit... heavy and very strong.
Have you read the JB CORN books?
JB CORN was one of the first "modern" haunters and, if I remember correctly, he came from a theatrical background, as well.
The books are a little out-dated but the stuff on wall construction is still viable.
The books are FREE (!) and available for download here: