This is the US Synchro model of the Kodak Brownie Reflex, which was manufactured from 1941 to 1952 and originally sold for $6. Here’s a link to the manual:

Model: Brownie Reflex

Type: Pseudo-TLR

Shutter Speed: I (instantaneous), 1/30 sec, and B (bulb)

Shutter: Rotary

Lens: Meniscus, non-focusing

Aperture: fixed

Film: 127

Picture size: 4×4 cm

Exposures Per Roll: 12

Designer: Henry O. Drotning

Place of Production: US & UK

Dates of US Production: May 1940 – May 1952, Synchro model released Sept 1941

Dates of UK Production: 1946 – May 1960

Other Features: Folding hood main lens and a second-surface keystone reflecting mirror viewfinder, Bakelite body, Original Price $6

The design was patented in 1940 by Henry O. Drotning (US Patent D119931).