If every piece of ice and snow on land were to suddenly melt, sea level would rise somewhere between 200 - 250 feet. That really isn't much, and would leave plenty of land very habitable for humans and our civilization.

You don't need to flee to Kazakhstan or Mongolia. If I did need to flee to Mongolia, I would rather commandeer a cruise ship and live on it as a floating city.

anywhere above 300 ft above sea level will be safe

Sea level is already rising. Overall, no area on the continents is safe from being submerged by oceans or epicontinental seas, aside from mountain ranges and plateau regions. Also, the rate at which the sea level is rising is minor to a human's perspective. We simply don't live long enough.

on the beach