n. A relationship that consists mostly of flirting.
Rather than go with the cliche of "we're good friends", which may not be the entire truth but is certainly truer as compared to the fact that we are not in a relationship, this wonderful new discovery, "flirtationship", is a much awaited fill in the blank.
—Pooja Bedi, “Heard of flirtationship?,” The Times of India, September 21, 2012
I think the average high school relationship probably lasts two weeks. Raging hormones and a desire to be the center of attention keep most teenagers moving on quickly, having mostly "flirtationships" and never really settling down.
—Courtney Phelan, “Phelan: High school relationships not always easy,” Kane County Chronicle, August 02, 2012
1994 (earliest)
When the real Sharon Stone (playing herself, fabulously as always) has a fling with fictional late-night talk-show host Larry Sanders (Garry Shandling as a Carson on Prozac), a star is shorn - of self-esteem, of dignity….

Not that their randy flirtationship is built on false pretenses. It's all pretense.
—Matt Roush, “Stone's ripple effect on 'Larry',” USA Today, August 10, 1994
In times when he had fivers by the fist-full
And fires of youth — where now are only embers.
Jack's Jills ! Why, Muse possesses quite a list full.
May's Jill, and June's Jill, August's, and September's….
Yet dares no more than skim each light adventure
Which followed on flirtationship's indenture.
—Gilbert Frankau, “One of Them,” The Poetical Works of Gilbert Frankau, February 01, 1918 (OED)