Back-formation from unflappable.
flappable (comparative more flappable, superlative most flappable)
- (informal) Capable of becoming flustered or upset.
1994 July 25, Jack Winter, “How I met my wife”, in The New Yorker:
There were two ways about it, but the chances that someone as flappable as I would be ept enough to become persona grata or a sung hero were slim.