RORY: That is the closest to a farm that I ever wanna get.
LORELAI: Amen, sister friend.
As far as I’m aware, “Amen, sister friend” is 1990s American slang to give encouragement or validation to a female friend, with “sister friend” implying a bond as close as sisters. Please correct me if I’m wrong!
It’s interesting that Amy Sherman-Palladino, the writer, uses this phrase, since she conceptualised the relationship between Lorelai and Rory as partially based on her imaginings of what a relationship would have been like with her dead sister, that she never knew.