The quality or state of being buckish; the affectation, showiness, or rakish manner characteristic of fashionable young men.
From 'buckish' + '-ness' (suffix forming nouns of quality or state). This abstract noun developed to describe the overall character or demeanor of affected fashionability.
Buckishness is basically the noun form of trying too hard to be cool—it's the 17th-century version of what we might now call 'peacocking' or 'thirstiness.' Writers of the era used it as a mild insult for excessive affectation!
Complete word intelligence in one call. Free tier — 50 lookups/day.