Since last March 1, the Italian government has reopened travel to former list E countries, among which are almost all African destinations, including Kenya. Since March 31, other news has been added, after Kenya, with some limitations, also accepts the unvaccinated.
It is possible to return to travel without restrictions, other than those suggested by the Farnesina and found on the pages of the individual countries on the viaggiaresicuri.it website and those imposed by the countries of arrival chosen by Italian travelers.
NO MORE PCR FOR VACCINATED PEOPLE
Kenya has removed the requirement for those vaccinated with at least two doses to make PCR swab no more than 72 hours before departure.
You can leave for Kenya without swab, always making sure that your airline confirms that it is not her to require it or any of the countries of the airports of transit. 
In any case, as is now well established, as a result of the suspension of previous orders and in view of the end of the state of emergency, not only tourists can go to Kenya, but are abolished also the obligation of quarantine on return and the PCR swab to be presented upon arrival.
In addition, Kenya no longer requires the molecular swab, nor the antigenic one moreover, when you have to leave the country. So it remains only the obligation to have certificate of at least two vaccinations, or Green Pass (also from healing, with limitations of validity that we report below).
ALSO THE UNVACCINATED CAN ENTER KENYA, PROVIDED THAT:
Even unvaccinated people can, for the first time, travel to Kenya. For them, the dynamics are still quite complex. You need the PCR swab that is needed both to leave from Italy and to arrive in Kenya, upon arrival in Kenya will be required to a swab antigenic (cost $ 30) at the airport and in case of positivity to a PCR ($ 50) that if confirmed positivity would force the traveler to isolation in the home reported on the visa online.
FURTHER: The Embassy of Kenya in Italy warns that for the unvaccinated is required a certificate stating the reasons why you could not be vaccinated. How to say that are accepted reasons for health (healing, inability to other diseases, etc. ...) but not those conceptual.

Let's recapitulate then the obligations in force in Kenya to access it.
DOUBLE VACCINATION CERTIFICATE OR GREEN PASS
First, it will be necessary to upload the certificate of double vaccination (it is not required the third or any other "booster") on the site globalhaven.org. Then, however, submit the relevant paper. For those who have a Healing Green Pass and have not done the vaccinations, the globalhaven.org website does not accept this option, so both the Embassy of Kenya in Rome, and the Kenyan airport authorities, recommend first of all to contact your airline to make sure it is aware of the new provisions, and then to print the Healing Green Pass and bring it with you. It is considered valid by the Kenyan authorities if it is no older than 90 days (source: Africa CDC, taken from the Embassy of Kenya in Italy, and you can print it out here and bring it with you just in case). Kenya also does not require vaccinations for minors.
PCR SWAB NO LONGER MANDATORY
To board a plane with final destination Kenya, if fully vaccinated, no longer need to be equipped with a certificate of negativity by PCR swab. It is advisable, however, to make sure that the airlines are on this line and do not require the swab and if any transit airports do not force passengers to arrive with the results of any test.
Moreover, since March 12, a mask is no longer compulsory in open places in Kenya.
As it is known, Kenya accepts tourists from Italy, and the immigration office present in the airports of Nairobi and Mombasa, will stamp the tourist visa equivalent to the date of return indicated on the online visa, unless otherwise indicated by the tourist, up to 3 months.
The same tourist visa will then eventually be renewable for another 3 months, but only online.
The cost of the visa is 51 USD, which with the transaction becomes 53, so at the current exchange rate of 48 euros.
We would like to remind you that it is no longer possible to apply for a paper visa on arrival in Kenya, and that in order to fill in the visa online you must go to the link evisa.go.ke on the Kenyan website. The practice can be resolved even in 24 hours, so it is recommended to make the visa at least two days before leaving.
JITENGE: You may be required to download the "Jitenge Moh" APP on your cell phone and report your destination. If so, just type Jitenge Moh App into Google and it will come up with the app to download and then follow the directions.
TO RETURN FROM KENYA
From March 1, 2022 to return from Kenya, as mentioned the Italian state no longer requires neither buffer nor quarantine. It will be enough to show your green pass. FROM MAY 1, 2022 IT WILL NO LONGER BE MANDATORY TO FILL IN THE PDF. As well as the airport authorities are not required to ask for PCR swab on exit. The important thing, as at departure, is to make sure that your airline does not ask for it.