I might or might not be your client, but I always thought a "flatolet" was just a regular 'olet designed to go on a large radius, essentially flat, header. Take a look at
. This table lists which Bonney Forge 'olets can go on what range of headers. For example a standard weight weldolet with a 1" outlet (branch) needs to be ordered based on what the run size is. Since the change in curvature gets less with larger sizes, the same 'olet may be used for multiple run sizes. A 1" 'olet which you'd put on a 6" run pipe would be the same 'olet that you'd put on a 10" run. For a 12" run, though, you'd have to get a different 'olet made to match the larger branch radius (lower curvature). That 'olet will work for up to a 36" branch. Beyond that, the curvature is effectively nil and your radius infinite: In this case, the run is "flat" and that's where the term "flatolet" comes from.
I agree with JTE, that is what I always heard and specified as a "flatolet"...a olet that due to branch size being so small and run size so big that the fitting was basically flat on bottom. More a type or subclass of Threadolet, sockolet, or weldolet that a unique fitting.