Are the files opening directly into Photoshop, and not via Camera RAW? If the latter was the case, then your ACR might be set to open in 16 bit for instance. But you mention flaterning the image before resaving, so you are obviously using layers, and that's probably what is causing the save to default to PSD.
How are you flaterning the image? Try using the keyboard shortcut 'Ctrl (Cmd) Shift e'. That works for me, but so does using the layers menu.
What sort of editing are you doing? And what version of Photoshop? The JDI (Just do it) feature that allows a 16 bit image came in a couple of versions ago, but you still need to select JPG from the drop down, even if you can skip the Image > Mode > 8 bits/channel step.