The function that controls profile menu is
{jrProfile_menu}
Docs: "{jrProfile_menu}"
https://www.jamroom.net/the-jamroom-network/documentation/module-developer-guide/1997/jrprofile-menu
In the iSkin its found in the
profile_header.tpl file around line 120 ish. It does have an order set and looks like this:
{jrProfile_menu template=$menu_template profile_quota_id=$profile_quota_id profile_url=$profile_url order="jrAction,jrBlog,jrCombinedAudio,jrAudio,jrCombinedVideo,jrVideo,jrGallery,jrGroup,jrEvent,jrYouTube,jrVimeo,jrFlickr"}
Recommended that you clone the skin to your own skin before making changes:
Docs: "Creating your own Skin ( Clone from an Existing Skin )"
https://www.jamroom.net/the-jamroom-network/documentation/skin-design-guide/839/creating-your-own-skin-clone-from-an-existing-skin
Or use the Template Editor to make the change:
Docs: "Using the Template Editor"
https://www.jamroom.net/the-jamroom-network/documentation/jamroom-admin-handbook/3183/using-the-template-editor
So your changes survive updates.