He didn’t. He assumed that the FBI could make the press believe Flynn lied, and thereby cause trouble. The media reports made Pence believe it, leading to the firing. The subsequent persecution b6 Mueller et al broke Flynn’s finances, and also threatened to incarcerate his son, whether his son had done anything wrong or not.
If they were able to railroad Flynn on such garbage charges, his son would be dead meat.
According to Pence it wasn't the media reports, it was Flynn.