Doing something with flying colors refers to getting a great success in doing it. flying colors据说来自于航海术语, colors在当时指飘扬着的海军军旗。当一艘战舰凯旋而归时，就会用军旗飘扬来表示胜利。沿用今天，flying colors表示成功地做了某事。

Examples:

She passed the GRE with flying colors. 她漂亮地成功通过GRE考试。

They launched their new products in international market with flying colors. 他们成功将新产品打入了国际市场。