That's a bit different. Galleries are generated on display and have a unique id per session. So just copying the button will not work here. You will not be able to move it around unless you modify the template files and are just moving it around within its tab already. Best I can suggest is create a Joomla menu item to it and then have a button that links to that menu item. To do this create a menu item with menutype Community Builder > Plugin then select CB Gallery for Plugin. Leaving everything default should send them to their profile gallery.
This does give me an idea on how I can improve the CB Gallery Bot to provide substitution usecases for linking to galleries though and added a feature ticket for that.
forge.joomlapolis.com/issues/6908