1) Blowhard 2) Boastful 3) Boastful individual 4) Bragging 5) Braggy 6) Crowing 7) Exaggerator 8) Exhibiting self-importance 9) French word used in English 10) Horn tooter 11) Proud 12) Self-aggrandising 13) Self-aggrandizing 14) Self-glorifier 15) Self-inflated one 16) Thraso was one 17) Vainglorious sort Found on https://www.crosswordclues.com/clue/braggart
Brag'gart noun [ Old French bragard flaunting, vain, bragging. See Brag , intransitive verb ] A boaster. « O, I could play the woman with mine eyes, And braggart with my tongue. Shak. » Found on http://www.encyclo.co.uk/webster/B/90