English Translation
The fine arts flourished in Italy in the 15th century.
栄える is not a good collocation with 美術. We often use 栄える as in 国が栄える because the connotation of 栄える is economically great and expanding. My alternative translations are:
15世紀のイタリアでは、美術が隆盛を極めた。（りゅうせいをきわめた）
15世紀のイタリアで美術が興隆した。（こうりゅうした）
イタリア美術は15世紀に全盛期を迎えた。（ぜんせいきをむかえた）
隆盛 and 興隆 are synonyms. But the first sentence with 極めた means the fifteenth century was the peak of Italian art. The third sentence with 全盛期 (the golden age) and the first one are interchangeable.
The second sentence, on the other hand, means “to being flourished during the fifteenth century” but doesn’t necessarily means the fifteenth century was the peak.
Neither of them talks about how much the fine art industry made profits. They purely describe how actively the fine art industry produced masterpieces.