I need some opinions here, I have a Mossberg shotgun with a AR stock adapter and full length receiver rail. I have a red dot on it but would also like an option to use iron sights on it. I cannot use ghost rings due to the height/placement of the rail. Would a set of AR-15 BUIS sight be practical? I am guessing that any set of front and rear sights would work? If this is practical does anyone have any recommendations as to brand, I do not need anything that fancy. I would also prefer the flip up type.

It would work - IF you can get the front sight at the proper height.

Are most of the AR-15 models designed to sit at a different levels (between front and rear)?

Quoted: Are most of the AR-15 models designed to sit at a different levels (between front and rear)?

AR sights are all designed to operate off the same height.  They know how tall the fixed front sight is and how tall the receiver rail is, so they build their rear sights to that height.

IF you're going to attach it to a shotgun you gotta make sure the front sight height is compatible with the rear sight height.  Probably the easiest way to do that is make sure your rail runs the entire length of the shotgun - then use a front sight that is intended to be used on a Free Float rail (YHM and Troy both make one as I'm sure do others).