I am helping a friend trace his roots. Is the name FLEISHMAN German
Yes.
It means flesh + man, probably butcher.
or could this family come >from another country?
Yes. [Your "or" is wrong.]
.. because it is also Yiddisch, and the Ashkenaziem used Yiddish/German familynames for civil use all over Europe, and even far into Asia. -- Evertjan Hannivoort. The Netherlands. (Please change the x'es to dots in my emailaddress)