I try to answer you with what I understood.
You would like a 'edit' task button on the item FLY page. Correct ?
I help you with the code, because you are new here so I write it for you.
Just add a toolbar button in the view :
Fork you view file (FRONT / ITEM). (view.html.php), the function displayXxxx(), where Xxxx is the alias name of your FLY template.
In this function you will find the toolbar definition.
Do not copy it all in your fork, just do :
protected function displayXxxx($tpl = null)
{
// Keep the call of the original code, and fork AFTER
parent::displayXxxx($tpl);
// Define the CUSTOM task button, because Jooma do not propose it in native (who wants to PR that ?)
// TODO : Enter the name of your view in the first parameter before the '.'
// TODO : The last parameter should be a language string.
CkJToolBarHelper::custom('[ViewName].edit', 'edit', 'edit', 'Edit');
}
I even tested it and it works for me.