So . . . why did the Obama administration decide to investigate Flynn, resulting in the FBI interview?

I believe the explanation is threefold: (1) to punish Flynn, and derivatively the incoming Trump administration, for opposing Obama’s anti-Israel legerdemain in the Security Council; (2) to promote the political narrative that Russia–Trump collusion had cheated Clinton out of her rightful election victory; and (3) to tie this collusion narrative to sanctions relief, thereby making it politically impossible for Trump to roll back Obama’s sanctions once he was sworn in — a boon for the Democrats’ collusion narrative since the sanctions stand as a reminder of Russia’s election meddling.

The ongoing Mueller probe is not a good-faith investigation of suspected espionage or other crime. It is the exploitation of the executive’s intelligence-gathering and law-enforcement powers in order to (a) criminalize Trump political policies with which the Obama administration disagreed and (b) frame Clinton’s electoral defeat as the product of a traitorous scheme rather than a rejection of Democratic-party priorities.