to pay no attention to (while listening); to take no notice of; to ignore; to let go in one ear and out the other
上司の小言を聞き流した。
I let my boss's grumbling go in one ear and out the other.
批判を聞き流しているとトラブルになる。
Ignoring criticism will only lead to trouble.
同僚の噂話は聞き流すのが一番だ。
The best approach is to tune out coworkers' gossip.