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1.
A friendship that has a potential to be a fling.
JD, you should totally start a flingship with Eliot. She's like your best friend and she's totally banging material.
von Eliot Reed 27. November 2011
 
2.
A flingship is a platonic friendship, usually of two females, characterized by the same parabolic curve of interest and intensity that defines classic romantic flings. Flingship participants spend increasing time together, followed by an intense crescendo, then an abrupt (and often painful) fizzle. Flingships, which are frequently born of the common interests of work or school, are common in big cities with high transplant rates, such as San Diego and NYC.
Erin and Jamie meet in physics class, where they become fast friends, drawing naked pictures of the professor and going to the coffee cart during breaks. They begin to go to happy hours together, text during work and introduce each other to friends and family; they are almost considered best friends...and then suddenly, when the term ends, they cease spending time together almost entirely.

Flingships also terminate when said "friend" sleeps with other friend's significant other.
von Dr. Evil 518 6. Dezember 2010