How can I create a login form to link to my store and customer database?

You cannot do that here at Jotform, a workaround solution would be to use the source code of the form and then apply some sort of programming code. See these guides:

http://www.jotform.com/help/126-How-to-send-Submissions-to-Your-MySQL-Database-Using-PHP

http://www.jotform.com/help/237-PHP-Forms-Explained