How to add the Interest field in profile page which links the user with similar interest?
This is done using taxonomy and the term reference field. Each term assigned to an entity has the option in the display mode to be a link to the term page, which in turn shows all entities tagged with that term. 

Edit-

Since default term pages only look for content entities you will have to create a view to override those term pages to show user entities instead. You  can use the taxonomy views integrator module to selectively choose which terms use which view. https://drupal.org/project/tvi