With the latest update, the Query User Profile action lets you get the manager quite easily : Assigning a Task to an Office 365 Manager
I actually created a similar blog post myself regarding app permissions and the web service call in O365 here: O365 - Call HTTP Web Service failed - Unauthorized "Access denied"
Which may be helpful for others trying to invoke these calls on different sites.
Thank you for sharing! I have marked your answer as correct.
Butting in for a sec, everyone: In merging spaces two days ago, links created prior have been broken. This was unintended and I'm working on a fix. All content is still available, but it will require using the "@" and then typing in keywords or search for the link. Failing that, visiting a person's profile page and clicking content will lead to all of their content. You can also find your own by clicking your avatar in the upper-right corner and selecting "Your Content" from the dropdown. Apologies for the hassle, but don't give up if a link seems dead at first blush, as Francois didn't in the reply above.
Your community manager
I have recently got the opportunity to give this a try based on partner request to query user profile properties from within Nintex forms. I came to realize whenever you invoked the Sp.AppContextSite(@target)/SP.UserProfiles.PeopleManager you will get into the error "Cannot find resource for the request SP.UserProfiles.PeopleManager" from the appweb add-in. This looks to me an issue caused by add-in permission related to the user profiles. To allow user profiles lookup in Nintex Workflow, add-in has built in allowing the administrator to request access to user profiles, and trust the add-in for granting access to the add-in to user profiles. I believe manually granting permission to the Nintex Form with access rights to the User Profiles likely to overcome this error... but I have so far get no luck on that yet..... should this be considered as bug, issue, enhancement, or new feature, to request, Euan Gamble?i will continue to check.... but if anyone has other thoughts or finding to share.