If you don't see the -item- edit button in the frontend of your site, there are multiple reasons for it:

• You do not have enough permissions to edit the item.
  with FLEXIaccess: you must be at least "registered" and you must have edit or editown permissions for this content (or its main category).
  without FLEXIaccess: you must be at least "editor"

• This is not supported for earlier versions, in this case the user needs to click to view the item, and then the edit button will be displayed at the top of the item (next to item's title).
  You are on a category view, using FC v1.5.5 or earlier
  FLEXIcontent v1.5.6 and later, has a new category parameter,  to show edit button for all items the user can edit in the category view.

• Your custom template does not have the edit button.
  
  To do that, for item view:
  -- edit components/com_flexicontent/templates/your_template/item.php
  -- add the the code, that is used in file components/com_flexicontent/templates/blog/item.php
  
  To do that, for category view:
  --edit components/com_flexicontent/templates/your_template/category_items.php
  -- add the the code, that is used in file components/com_flexicontent/templates/blog/category_items.php