There are a few requirements to move your CYGWIN compiled COBOL programs to a flash drive for running on a different computer. Why would you want to do that?
You may have a production machine the programs are targeted for that you do not want to include the source files.
The easiest way to get setup using a USB Drive is to have CYGWIN already installed on the machine and add the GNU Cobol DLL to the path.
Create a portable CYGWIN USB using these instructions for CygwinPortable.
https://github.com/GathSystems/CygwinPortable
2 Required Files to run GNU Cobol from a flash Drive can be found in these locations.
D:\cygwin64\usr\i686-pc-cygwin\sys-root\usr\bin\cygwin1.dll
Older path:
E:\cygwin64\usr\i686-pc-cygwin\sys-root\usr\bin\cygwin1.dll
Newer Path:
E:\cygwin64\bin\cygwin1.dll
cygcob-4.dll (GNU COBOL DLL)
Packaged path:
gnu-cobol-2.0_nightly_r658.tar\gnu-cobol-2.0_nightly_r658\gnu-cobol-2.0\libcob\.libs\cygcob-4.dll
Installed Path:
E:\cygwin64\usr\local\bin\cygcob-4.dll
Once you have included the 2 DLL files with your program files you should be able to add the path to the targeted system and run your program.