Flattening should be expected to make files bigger, much bigger in the worst case. It is rarely a way to reduce size, though sometimes it will be - it all depends on what is in the file.
An example where it could reduce size is where a series of images are overlayed transparently. This would end up being a single one. There may be cases where lots of layers get consolidated into something simpler, but if the layers were vector and the result is raster it won't.
So, flattening might be a useful tool, but it's best to try it and test the result.
Better still to stop the proprietary software from choking... !
By the way, I can't think why flattening a second time should do anything either.
You should probably be using Audit Space Usage before deciding what to do (and also to see what happened in this case).
Are you doing a Save As rather than a Save after you do the work. The Save keeps all of the changed items. Save As clears the old stuff out of the file. I am not sure with preflight, but worth a try.