After the announcement, the department was flooded with enquiries from the public.

was 是 be 动词的过去式，表示被动语态。 flooded 是动词 flood 的过去分词形式，原意是"洪水淹没"，这里用作比喻表示"大量涌入"。 with 是介词，表示"伴随、带有"。 was flooded with 这个被动结构字面意思是"被...淹没"，引申为"收到大量..."，用来形容某事物突然大量出现的情况。