Coils will have two straight edges on opposite sides.
Booklets of this issue are 2 stamps wide and 3 stamps high, with the binding tab at the top, so booklet singles will have a straight edge along one side, or along a side and bottom combined.
So yes, your stamp must be from a sheet. Odds are flat plate. It takes very careful measurement to distinguish flat vs rotary - best done by using another stamp of known production methods and NOT a ruler of any kind.
As a "postal history" aside, the Forked River, NJ machine cancel is from a machine made by the B.F. Cummins Co. and known used there at least 1912-1936, an unusual arrangement to have a year date within the killer bars instead of within the dial.