This was a brief experiment based on migration data in the
UN Demographic Yearbook. It attempts to show the percentage of people born in a country that currently live outside the country.
Unfortunately, it's largely a failure because the data is all kinds of unreliable. Data on native population (Volume 3, Table 1) is missing for more than half of all UN member states. Data on which country expatriates were born in (Volume 3, Table 2) is extremely spotty, and dependent on national censuses that use widely varying classification schemes.
This list shows the calculable percentage of the native-born population living elsewhere for the 87 UN member states for which some data was available.