The phrase 'flying colours' is often used to signify success or achievement in a particular task or endeavor. There are several synonyms for this phrase, including 'triumphantly,' 'successfully,' 'with flying colors,' 'victoriously,' 'in triumph,' and 'in glory.' These words convey a sense of accomplishment and pride in completing a task or achieving a goal. 'With flying colors' can also refer to doing something with great distinction and excellence, making it as one of the best in a group or category. Whatever the synonym used, the idea is that one has excelled or accomplished something significant.