As I understand the case, Flynn wasn’t being investigated in the sense of being suspected of committing a crime, but was being interviewed as part of a counterintelligence investigation of Russia. He’s guilty of lying about his contacts with the Russian ambassador and discussion of sanctions in a way that materially impeded the counterintelligence investigation.
The implication is that Robert Mueller had enough evidence to suspect but not prove that Donald Trump was aware of Flynn’s contacts and felt that Flynn’s lies prevented him from finding out. So, Flynn may have lied to prevent a Russia investigation from turning into a Trump investigation.
Any mention of the Logan Act feels like a red herring. It was explicitly said not to be one of the charges that were being considered before a plea deal was reached.
All this can be gleaned from documents that Wheeler links to.