Sharepoint PowerApps Contact Details from Persons Column

SetvarCurrentUserExis 

One potential solution.

This is the list in question:

Within the Power App built from your list, add an additional data source
(Office 365 Users, to get the business phone details)

'OnVisible' of the Edit Screen set a context variable, which is intended to keep track of the result for the user search against the Officer 365 connector. The 'DataCardValue5' is in my case the Person column form field.
Copy and paste the same formula into the onChange property of the 'DataCardValue5'.

UpdateContext({SelectedPersonLookup : Office365Users.SearchUser({searchTerm:DataCardValue5.Selected.Email})})

The default value of the DataCardValue4 (my e-mail field) would then be

First(SelectedPersonLookup).Mail

 and for the Phone number (which could included multiple numbers)

First(First(SelectedPersonLookup).BusinessPhones).Value

Additionally you could think about removing the option to manually alter the e-mail and phone number by changing the DisplayMode property of both form fields

Nevertheless you might need to adjust this solution furthermore, depending on your requirements.