Okay, let’s say that the accusations against Flynn are totally true.
A lame duck President Obama has imposed fairly serious sanctions, including expulsion of diplomats, on the laughable premise that the Russians hacked the DNC and John Podesta. A key feature of the Trump campaign has been the development of a better relationship with Russia. But the outgoing President has sabotaged that.
So Flynn asks the Russians not to overreact, that President Trump will take another look at those sanctions. The message goes up the chain and President Putin decides to postpone any retaliation. This makes Obama look reckless and vindictive and Putin looks like the reasonable leader.
How does that hurt the US? If anything, it smooths the way to a better relationship with Russia and a reduction in the risk of war.