If you’re a flingee, it means you’ve just had something thrown at you. I’m sorry.
Words like this, i.e with the suffix ‘ee’ (the bit at the end), generally indicate that someone’s got something from someone or something else – or has received the action of a verb, if we want to be smartarses about it. So that’s words like:
If that hits me, I’m going to punch you in the face
interviewee – you’re getting the interview
employee – you’re getting the employment (you must have aced that interview)
trainee – you’re getting the training
payee – you’re getting the payment, lucky you (must be all that employment and training).
(Other non-employment ‘ee’ words are available.)
Back to ‘flingee’. The word ‘fling’ probably comes from an Old Norse word, ‘flengja’, meaning ‘to whip or flog’. Over time it came to be associated with sudden, impulsive movements or actions, which is how we got ‘fling’ in English.
No one’s quite sure how ‘fling’ came to describe brief romantic liaisons, although that didn’t come about until the late 19th or early 20th century (the meaning, not the flings – those have been going since time immemorial). Maybe it’s something to do with throwing stuff being impulsive and fun? (There’s a tossing-off joke here, but I am of course far too mature to make it, so I’ll just leave that with you.)