“自吹”的英语可以翻译为：preen oneself，boast of ...

他总是自吹他的小孩是多么聪明.He's always boasting about how clever his children are.自吹有学问,实际是无知.He who boasts of his knowledge proclaims his ignorance.他自吹他是最好的.His boast is that he's the best....