If you don't see the -item- edit button in the frontend of your site, then most likely reason is:
user does not have enough permissions to edit the item.
(J2.5-J3.x+)
1. User belongs to (1 or more) user group(s) that have been explicilty denied editing to
- to item itself
- to item's main category (or to any parent category or to FLEXIcontent component)
- to item's content type (YES you can allow/deny editing per content type too)
2. User does not belong to a user group, that has edit privilege:
- in item's main category (or to any parent category or to FLEXIcontent component)
- in item's content type
... thus by not having privilege he/she is "soft-denied" edit access
(J1.5)
1. with FLEXIaccess: user must be at least "registered" and you must have edit or editown permissions for this content (or its main category).
2. without FLEXIaccess: you must be at least "editor"