I have in my armoury a flat Stubbs file which is 0.6mm thick. The faces are smooth, the cut being solely on the edge which is flat. Stubbs files have long since disappeared except on the second-hand market where they are akin to hens' teeth.
The nearest equivalent I have found are Luthier's nut files, used for making the grooves in stringed instrument bridges and top of the finger board to take the strings. I have a few which are 10, 13, 16 and 20 thou thick. These cut only on the edge but, unlike the Stubbs, the edge is half-round. Nevertheless, I find these very useful, especially the 13 thou which is the same thickness as most brass etched sheets for 4mm models. I did not find them easy to source in the UK (it was a few years ago) and bought mine from
Stewart Macdonald (Stewmac) in the US. They are about $25 which today is around £18.50 (plus the inevitable p&p). I got mine when I was in the States.
Returning to fine shaped files, I have found this
'ultra thin' (0.6mm) fine round file from Metal Clay in Dorset at £22. There is also a medium cut round and
flat file which is 0.5mm thick.