boast
夸 centers on exaggerated self-praise: boasting or bragging about oneself in an inflated way.
夸 combines 大 (big) with 亏, which is thought to represent an extended or exaggerated breath or sound, together suggesting loud, exaggerated speech or boasting.
A big 大 person with an open mouth 亏 is loudly boasting about their achievements.
For コ, imagine a boastful person shouting 'Co!' as they exaggerate: Co -> コ, like a loud, short exclamation of self-praise.