To update a user account you need to ensure that “Allow Update User Account” in the Environment config is selected, and that your user has the right permissions (in Accounts/roles in Permissions) to update a user. Also, ensure that you are using the “update user account” action node.
With these settings, updating a user’s phone number should be possible. Let me know if the problem persists.
It seems that you are trying to update the user phone number directly? If so, a good way to avoid the read only trouble is to add a runtime attribute to a related “person” object or in the app variables and on update that attribute with det User.phoneNumber on edit/dialog open etc. On save you use the update User action node, as Isabel stated, to map the phone number from the person.phoneNumber to the User object.