Traveling from Italy to Kenya ahead of the summer vacations is becoming increasingly easy for Italians, and it is especially so when it comes to the return journey, since as of last June 1 our country no longer requires a green pass, related vaccinations or any equivalent certification when entering our airports.
Clearly, as the Italian (travel safe) and Kenyan (Ministry of Health) sites also remind us, one must comply with the rules in force in the country of arrival as well, not just those for returning home.
But even here for the past three months it has been possible for unvaccinated people to enter through airport customs in Nairobi and Mombasa and spend a maximum of 90 days (renewable online) in the country.
So here are all the rules in and out of Kenya, summarized in one article!
NO MORE SWABBING FOR VACCINEES
For those vaccinated with at least two doses, travel now does not require a PCR swab, either by the two governments or by the airlines (best to inquire, however, because rules change often, especially for airport transits).
Same for return quarantine: under no circumstances (unless with symptoms attributable to the virus and after swabbing upon arrival) will quarantine be required. Just as there will be no more need to submit the swab, either molecular or antigenic, on arrival, nor to do so before leaving. 
Like Italy, Kenya no longer requires the molecular swab, nor the antigenic swab moreover, when you have to leave.
So all that remains is the requirement to have certificate of at least two vaccinations, or Green Pass (also from recovery, with validity limitations that we quote below).
EVEN THE UNVACCINATED CAN ENTER KENYA, PROVIDED:
Even the unvaccinated can, for the first time, travel to Kenya. For them, the dynamics are still quite complex. It takes the PCR swab which is needed both to depart from Italy and to arrive in Kenya, upon arrival in Kenya one will be required to take an antigen swab (cost $30) at the airport and in case of positivity a PCR ($50) which if it confirms the positivity would force the traveler into isolation in the domicile reported on the online visa.
IN ADDITION: The Kenyan Embassy in Italy warns that for those who are not vaccinated, a certificate is required stating the reasons why one could not be vaccinated. As in, health reasons are accepted (recovery, inability due to other illnesses, etc...) but not conceptual ones.
There will not be, on departure from Italy, to fill out the Passenger Locator Form, but only upload the double vaccination certificate (no third or any other "booster" is required) on globalhaven.org. Then still submit the relevant paperwork.
For those who have the Green Pass from healing and have not done the vaccinations, the globalhaven.org website is unlikely to accept this option, so both the Kenyan Embassy in Rome and the Kenyan airport authorities advise first of all to contact your airline to be sure it is aware of the new provisions, and then to print out the Green Pass from healing and bring it with you. It is considered valid by Kenyan authorities if it is no older than 90 days (Africa CDC source taken from Embassy of Kenya in Italy with communiqué that you can print here and carry with you just in case). Kenya also would not require vaccinations from minors, but since it has also opened up to "no vax" all those over 5 years old, while not uploading it to the global haven portal, must present the vaccination certificate, or undergo PCR swab on departure and antigen swab on arrival, with additional medical letter. Pero any other information, look under the Kenya tab, on the Ministry of Foreign Affairs' viaggiaresicuri.it website.

So let's recap the requirements in place in Kenya to gain access.
DOUBLE VACCINATION CERTIFICATE OR GREEN PASS
First, you will need to upload
PCR SWAB AND PLF NO LONGER MANDATORY
To board a plane with final destination Kenya, if fully vaccinated, you no longer need to carry a PCR Swab Negative Certificate. However, it is advisable to make sure that airlines are also along these lines and do not require the swab and whether any transit airports do not force passengers to arrive with any test results.

ENTERING KENYA

As is well known, Kenya accepts tourists from Italy, and the immigration office present at the airports in Nairobi and Mombasa will stamp the tourist visa equivalent to the return date indicated on the online visa, unless otherwise specified by the tourist, up to 3 months.
The same tourist visa will then possibly be renewable for another 3 months, but exclusively online.
The cost of the visa is 51 USD, which with the transaction becomes 53, so at the current exchange rate 48 euros.
As a reminder, there is no longer the option of a paper visa upon arrival in Kenya, and to fill out the visa online, one must go to the evisa.go.ke link on the Kenyan website. The paperwork can be resolved in as little as 24 hours, so we recommend that you get your visa done at least two days before you leave.
JITENGE: You may be required to download the "Jitenge Moh" APP on your cell phone and report your destination. In case, just type Jitenge Moh App in Google and it will come up the app to download, and then follow the directions. 
Also, as of last March 12, a face mask is no longer mandatory in open places in Kenya.
TO RETURN FROM KENYA
As of June 1, 2022, to return from Kenya, as mentioned above, the Italian state, in addition to no longer requiring nor tampon, WILL NO LONGER REQUIRE GREEN PASS or related certifications.
FROM MAY 1, 2022 FURTHER, IT IS NO LONGER MANDATORY TO FILE THE PLF, as decided by Minister Speranza. (Article here: https://www.malindikenya.net/it/articoli/notizie/ultime-notizie/dal-1-maggio-niente-piu-plf-per-tornare-dal-kenya--.html)
Just as airport authorities are not required to ask for PCR swabs on departure. The important thing, as at departure, is to make sure that your airline or any transit airports do not demand it.