One man? Definitely not. A few? More likely, but still improbable.
The largest issue you would face is the nozzle spray size of the flamethrower. Vietnam era napalm flamethrowers were largely designed to get as much range as possible, making it effectively similar to a flaming squirt gun. While this is useful against less mobile humans, not so much for flying swarms as the spray area isn't very large. When shooting at a swarm in full flight, you would definitely hit a fair few, but the rest would just evade by flying to any side but down. When possessing a hive mind, this becomes significantly easier as well.
This could be offset by increasing the nozzle spray to something more like a garden hose. This would effectively create a wall of flame rather than a stream, which would be significantly more effective against a swarm. Especially if not as much power is needed to damage them, a little flame goes a long way against a creature that small. They might be resilient, but they can still be cooked.
The only unsolvable issue with a napalm flamethrower is this: You cannot shoot up. It doesn't burn efficiently enough, and residual flaming napalm would come back down, so if you shoot up, you will simply douse yourself in your own flame. And a swarm can fly, all they need to do is get overhead and descend upon you. If you barricade yourself in a room while spraying the entrance, you could defend yourself. But which hive mind would voluntarily run themselves to death in a sea of flames when they don't have to?
There is one significant advantage using a flamethrower could have against the roaches if the battle is drawn out: Smoke. This could disorient the roaches, and make them bump into each other making them vulnerable and less mobile. I this has been proven to work on bees and mosquitoes, but I don't know how effective it would be against a swarm of roaches.