In addition to everything said above, the placement and style of the "Dodgers" script does not correspond with anything seen on actual Dodgers uniforms during the 30s, 40s and 50s.
On all uniforms from 1949 forward the "d" is on the jerseys placket, not the "g". However, there are two exceptions, during the 48 and 49 seasons they wore a jersey that actually had the "g" on the placket, but a different script. And none of these Dodgers scripts have a notch in the "o" either. This image shows the different styles. Also, notice the piping on the sleeves, Robinson's jersey doesn't have it:
I'm pretty certain that this jersey is a pure fabrication. It might be an old flannel jersey, possibly even a jersey that has some kind of affiliation with the Dodgers but the lettering, the missing tagging all speak volumes against it being a Brooklyn Dodgers jersey. At over 300$ the buyer could've just as well bought a Mitchell and Ness replica.
I do wonder if it will pop up on the auction circus again.