Can I add the same phone someone else has already added as an authentication method for Duo Security?

Yes, multiple people can add the same phone. This might be convenient in a setting where a desk phone is shared by a group of people in an office.

Keep in mind that if the new person adding the phone renames it during the process, it will be renamed for all the users. This does not prevent you from using the phone as an authentication method; just be sure that it is the same device!