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I believe that in the link Mark posted there is mention and an image of a paddle strop the company produced. I would take it then that flat strop is the same as a paddle strop and why wouldn't they...

That is in very nice condition and a handsome addition to your collection. In case you have not researched Klauberg and Brothers Inc, here is a bit of info...

I have no idea why they would say to only use a flat strop or even mean by "flat strop". I do have the same type of razor, frameback, but without the removable blade option and use a hanging strop...