This 流しておいた means "I let it slide" or "I let the subject drop". It means to deliberately choose not to pursue the topic. The implied object of 流す is the topic (話題). The use of the adverb 緩く ("gently; softly") here seems a little atypical, but it seems to emphasize that the protagonist did so naturally, without drawing attention or sounding impolite.
- This 流す means to deliberately choose not to pursue the topic.
- The subsidiary verb (-て)おく is used to add a sense of "then let it go" or "then leave it in that state".
- The implied object of 流す is the topic (話題).
- The use of the adverb 緩く ("gently; softly") here seems a little atypical, but it appears to emphasize that the protagonist did so naturally, without drawing attention or sounding impolite. We more commonly say 軽く流す or さらっと流す.