How is Kakashi able to get Mangekyou Sharingan?
Short answer.

Sharingan wielders don't really have to be part of the Uchiha clan to activate the Mangekyou Sharingan.


  It is initially awakened by the trauma suffered from witnessing the death of someone close to the user.


So you just have to have a Sharingan and witness the death of someone close to you.

Sources:


Mangekyou Sharingan