you don't need a bt email address to get BTID any email address is ok so create one with gmail as sugested or outlook or hotmail or someone else
Was your friend not asked for an email address or offered the option to create one when he/she signed up to BT?
I believe they should be able to allocate a BT Mail address for you over the phone or live chat?
The BT help pages suggest a BT Mail address is optionally allocated at the time of placing the BT Broadband order, but there have been plenty of posts from customers who have ended up in a similar situation where they seem stuck without one. Sometimes the mods have helped to get things resolved.
You can use any other non BT email address with a BT ID, but not everybody wants to set up one with a different provider and who may or not have different rules about scanning messages or advertising via email. If you already have a different one available I think you can use it temporarily to get the BT ID set up, then set up a BT Mail address on-line, then amend your account to use the BT Mail one.