Unfortunately, using the 'Sign in with someone else's credentials' will not work from this screen - this will grant the emailing permissions to the Admin user that is signing in, which is not what is required. We are a little limited by how Microsoft deals with this unfortunately - and it appears that the only method that succeeds is assigning the user to the application directly, as it demonstrated below.
When setting up OAuth for Office 365, you can occasionally come to a screen that says you need Admin Approval - this indicates that within your Organisation, you do not have permissions to grant the authority for the P11D Organiser to send email.
One alternative option is to set up a Group with the user as a member, and then go to ADD > Enterprise Applications > Consent and permissions > User consent settings in the Azure portal and allow that group (and therefore user) to allow consent:
The Application Has Not Appeared
If the applications has not appeared to be assigned, one option is that you authenticate through the Organiser application using an Admin's credentials (not the user's and then escalated), then once approved for you, it would appear in the Enterprise application list for you to assign to the user.
Please note that the application won't appear in your colleagues 'My Apps' area until they are granted the permission.