Interesting - the august 3rd US embassy health alert (
https://tz.usembassy.gov/health-aler...august-3-2020/) states the following:
The Tanzanian Health Ministry put out a directive stating all travelers entering Tanzania are required to present a valid COVID-19 certificate from an approved laboratory in a departure country tested within 72 hours before travel.
But the august 7th alert (
https://tz.usembassy.gov/health-aler...august-7-2020/):
All travelers whether foreigners or returning residents whose countries or airlines require them to provide negative testing for COVID-19 as a condition for traveling will be required to present a certificate on arrival. Travelers from other countries with symptoms and signs related to COVID-19 infection will undergo enhanced screening and may be tested on arrival.
Which I guess means that no COVID-19 test is needed to go from Kenya -> Tanzania, since Kenya doesn't require any testing for *outbound* travel.