not sure other than he could have been a set-up just so Columbo could see Flemmings reaction. Also there was the bit, "he's lying, he didn't do it" I'm sure Columbo already knew that. It also could have just been a "twist" like a lot of mystery shows from 1968 did.

As far as I understand, he's one of those people who go around confessing to things they didn't do, and he gives off that kind of vibe, so Flemming (being a psychiatrist) has to say so.
Of course, he does halfway accuse Columbo of setting up the whole thing, so I'm not sure.