"川流不息地涌入" can be translated into English as "flow in ceaselessly" or "pour in continuously".
Both expressions convey the idea of a continuous and uninterrupted influx, similar to the Chinese phrase "川流不息地涌入" (literally "flowing endlessly and pouring in").
"Flow in ceaselessly" emphasizes the uninterrupted and steady nature of the influx.
"Pour in continuously" adds a bit more urgency or volume to the image, suggesting a larger or more forceful flow.
Choose the one that best fits the context of your sentence.