I want to use another user rather than SPFARM or Setup user for deploying wsp files in SharePoint farm so which database permissions are required to deploy wsp files
Below are right requires for WSP deployment. (though never tried without farm admins) but to answer your question, user should be below..
Site Collection Administrator
Member of the "local Administrators" group on each server in the farm (excluding DB)
Member of the DB_owner role on the SharePoint_Config DB and the content DBs for the Central Admin and web applications.
the Database permission level required to deploy a solution is
- on SharePoint configuration database.
- on SharePoint administrator database.
- on Content Database.
There are other permissions required but it's not related to the DB . please check What permissions are needed to deploy a WSP to SharePoint 2010?