According to Sugiyama, there were two Cosmoflex models, differing only by the shutter types used. This one
in my collection is the Model II, with an S Luna shutter, made by whom I know not. McKeown adds nothing, merely repeating Sugiyama's details. The company was Alfa Optical Co., but I have no other details, although Sugiyama also says they produced an "Alfaflex". There are four or five Japanese websites which may have more, but I'm afraid my Japanese is too limited!
Taking lens is S. Cosmo 75mm f3.5
Shutter is S Luna 1 to 1/200
Below mine is a Model I variant sold on eBay, with a TSK (Toyo S K Co.) shutter.
This shutter had no self-timer.