"川流不息地涌入" can be translated into English as "flow in ceaselessly/in an uninterrupted stream" or "pour in continuously".
Here are some example sentences for context:
People are flowing in ceaselessly into the city. （人们川流不息地涌入这座城市。）
Tourists pour in continuously during the holiday season. （在假期，游客们川流不息地涌入。）