He created his greatest works during the flourishing of his career.

flourishing 是动词 flourish 的现在分词形式，flourish 本意是"繁荣、茂盛"，引申为"处于鼎盛时期"。 这里用现在分词形式表示"正在蓬勃发展、处于全盛期"的状态，用来形容事业达到最高峰的阶段。