I had downloaded Visio 2013 Professional trial. I found icons representing database server and database. But I did not find anything related to instance. I have a requirement where I need to show like multiple instances on a single database server.

Can anyone he

There are many sources available for Visio shapes and stencils etc, and many of those are free.

Here are some suggestions:

http://blogs.technet.com/b/tothesharepoint/archive/2013/02/13/get-the-new-office-visio-stencil-with-the-cool-icons.aspx

http://joshrobi.blogspot.com.au/2008/08/useful-visio-stencil-set-for-sql-server.html

http://markgstacey.net/2013/02/11/visio-shapes/

http://www.microsoft.com/en-us/download/details.aspx?id=25110