I restored my '51 F-1 a long time ago, to be honest, I don't remember seeing the VIN #on the frame of the truck... I know my Flathead powered cars have the VIN on the frame, on the drivers side by the front cross member.
On late-51s and all 52s, there is no patent plate at the PS firewall near the horn relay. Instead they have an augmented plate on the glovebox door. The "official" serial number is on the top of the right-hand frame rail just behind the bracket for the engine support. It should read *F1R2XXYYYYY*
F1 = F-1
R = V8 (D for 215 OHV 6)
2 = 1952
XX = assembly plant
YYYYY = consecutive unit number
* = "Stars" at the beginning and end
Here's a handy decoder for 51 - 52