Fuel can only flow into the engine if leaking through the needle or possibly the impulse circuit. One of those is leaking.
On the pump side, the flat diaphragm goes against the carburetor, then the gasket, then the cover. On the metering side with the needle, the gasket goes on first, then the diaphragm, and then the cover. Make sure the needle lever is at the right height. You can polish the needle seat with a Q-tip cut on an angle and some toothpaste.
Depends on the era of the saw, but current tank vents don’t allow pressure to escape, they will only flow into the tank to allow air to replace fuel as it’s burned. So if it’s flooding, it’s not the tank vent. Although the way it sounds, you should probably replace the vent bits as well