Missing edit parent button in inline edit mode in the Flamingo skin

Steps to reproduce:
1. Go to wiki edit mode as a user with edit rights on a page, observe the edit parent button on the top right of the document content.
2. Go to the same document in inline edit mode, observe there is no edit parent button.
3. Go to inline edit on the same document but on the colibri skin (i.e. ?skin=colibri) and see that there is an edit parent button.

The code in edit.vm also suggests that this was overlooked when flamingo was implemented.