Are the hadiths about asking Allah for luck authentic? Does luck or chance exist? Is saying "coincidence" considered shirk? And is it permissible to use the phrase "stroke of luck"?

A hadith with the wording mentioned in the question has not been found. "Bakht" (بَخْت) refers to success and luck, which are meanings of "Jadd" (جَدّ) as stated in the two Sahih collections with the wording: "And the fortune of the fortunate will not avail him with You."