After his comeback concert, the singer was flooded with offers for new performances.

was 是 be 动词的过去式，表示被动语态。 flooded 是动词 flood 的过去分词，原意是"洪水泛滥"，这里比喻"大量涌入"。 with 是介词，表示"伴随"或"带有"。 was flooded with 这个被动结构表示"被...大量涌入"，在这里指"收到大量邀约"。