Synonyms of the word 
UNFLAPPABLE → COMPOSED - IMPERTURBABLE
unflappable
- adj. Remaining composed and level-headed at all times; unswayed by adversity or excitement; impossible to fluster;…
composed
- adj. showing composure.
- v. simple past tense and past participle of compose.
imperturbable
- adj. Not easily perturbed, upset or excited.
- adj. Calm and collected, even under pressure.
If you are interested in words, visit the following sites :
- wiktionary.org/unflappable For complete definition of a word
- 1word.ws/unflappable to play with words, suffixs, prefixs, etc.