I can only see the "Edit My Profile" link on the WP toolbar if I am logged in as an admin user, however I've like to allow other users to edit this as well.
I don't believe that I've configured anything to block this (I had a function to remove the toolbar for certain usergroups but even after removing that I can see the toolbar but not the edit feature). I'm not 100% that its Toolset which controls this but it seems possible since I'm using it for most things on the site and don't think I have any other plugins which could be responsible.
It is, yeah. We have two custom roles (Lender and Broker) so all my tests have been with them, though I'd tried assigning some test users additional core roles such as Author/Contributor and didn't it see it after that either.
FYI I'm now thinking I might just create a custom User form to handle the process of editing their accounts anyway, so don't worry about spending too much time on this, though if you have a quick answer it would be handy to know.
Haven't resolved the issue of the missing link but not entirely sure it's down to Toolset anyway, so have just gone another route of building an edit profile form instead.