The order of the Ministry of Health, which comes into force from Tuesday, February 1 until March 15, 2022, does not change the restrictions for the countries of band E of which Kenya is part. That is the band that groups the nations in which Italian citizens cannot go for tourism.
It is worth remembering that, despite the fact that controls have always been very mild and often some airlines report travelers not in compliance, by law those who leave for Kenya as tourists, with self-certification or fictitious letter of invitation, risk if discovered a fine of 600 to 2000 euros for false declaration or from 2 to 6 years imprisonment. There are some exceptions of course.
Here they are:
WORK: It means already having a work permit in Kenya and the corresponding stamp in your passport. Some compatriots have not been allowed to leave Italy because they did not produce evidence of their work permit, despite having submitted "screenshots" or printouts of the request to the Kenyan Immigration Office.
Others were detained because they were only in possession of an application for employment from a Kenyan company.
ABSOLUTE URGENCY: This category includes family reunifications with self-certification of urgency and documents proving the family relationship with Italians residing in Kenya or Kenyan citizens.  Regarding health problems, the decree is not very clear. It is advisable to ask at the Questura, the Ministry of Foreign Affairs or competent Italian offices.
Those who have done so, according to the news reported on malindikenya.net, have received the answer that these are, however, possibilities related only to those who are residents or Kenyan citizens living in Italy.
RETURN TO YOUR OWN HOME OR DOMICILE: Residents in Kenya who only have a residence permit (pensioners, etc. ...) can return if in possession of such a permit. Those who have a declared home in Italy could apply for a transfer to that home. But it is better to ask in advance in the Prefecture. Even regular rental contracts are accepted.
ALL OTHER REASONS MAY NOT BE ACCEPTED.
Following numerous reports, controls at airports are being intensified, as well as pressure on airlines that should carry out a first check on passengers. The second should be carried out by Italian authorities at passport control. Those who have a second home in Kenya or a regular rental contract or have proven reasons of urgency can prove it with a self-certification and attached documents and embark, subject to online visa issued by the Kenyan authorities.
By provision of the Kenyan Immigration authorities to the airlines, in fact, those who will not have the online visa will not even be boarded on a flight to Kenya.
The fact that many Kenyans are leaving anyway for tourism and are not checked at the airport is not a total certainty of possibility of being boarded. Sometimes random checks are made, sometimes a fussy employee at check-in can make you lose your trip and your ticket.
ENTRY INTO KENYA:KENYA ACCEPTS TOURISTS FROM ITALY
It will stamp to who arrives the tourist visa of 3 months renewable then for other 3.
The cost of the visa is always 50 USD or 40 euros.
Remember that to fill out the visa online you must go to the link accounts.ecitizen.go.ke/register/visitor of the Kenyan immigration site.
TRAVEL TO KENYA, OBLIGATIONS: 
To enter Kenya it is necessary to present at the airport in Nairobi or Mombasa the PCR swab (not serological, not other kind of analysis) carried out not more than 72 hours before departure for Kenya (rule modified on December 22, 2021). ALSO FOR GREEN PASS holders because at the moment there are no bilateral agreements between the two countries, nor between the European Union and the African Union or individual countries. SINCE DECEMBER 21, DESPITE A REQUEST FOR SUSPENSION OF THE DIRECTIVE BY THE HIGH COURT, ONLY HOLDERS OF VACCINATION CERTIFICATES ARE ALLOWED TO ENTER KENYA. CHILDREN UNDER 18 ARE EXEMPT.
So to be clear: PCR swab 72 hours before departure for Kenya, for everyone. No longer 96 hours from arrival as previously. SINCE DECEMBER 21, DESPITE A REQUEST FOR SUSPENSION OF THE DIRECTIVE BY THE HIGH COURT, ONLY VACCINATION CERTIFICATE HOLDERS ARE ALLOWED TO ENTER KENYA. MINORS UNDER 18 YEARS OLD ARE EXEMPTED.
WITH THESE REQUIREMENTS THERE WILL BE NO NEED FOR QUARANTINE IN KENYA.
QR CODE: You must obtain the QR code that will be scanned by Kenyan authorities to alert the Ministry of Health and other offices of your presence on Kenyan soil. You can get it by filling and sending this FORM: https://ears.health.go.ke/airline_registration/
GLOBAL HAVEN: Green Pass and TT CODE will need to be entered into the www.globalhaven.org portal. As of January 18, 2022, the Kenyan Ministry of Health has requested that airlines check that this is done. Even companies that previously did not ask for this entry, such as Ethiopian, are now asking for it. Be careful, you may not be boarded if you do not register in the portal.
RETURN
To return from Kenya, in addition to having to present at the exit in Mombasa or Nairobi the swab made 72 hours before (and doing so does not remove you from quarantine, which is still subject to occasional checks and your communication to the ASL through self-certification), from the Official Gazette of April 17, 2021 now you must submit a molecular swab (PCR) or antigenic carried out at most 48 hours before in the country of departure. In the difficulty of succeeding in Kenya to have a PCR done no later than 48 hours, the simplest solution could be represented by the PCR of 96 hours to exit and the antigenic of the day before to enter Italy.
It is therefore advisable to do always and in any case the PCR swab although until now nominally the obligation for the return boarding in Italy can only be requested by airlines and there are no official written communications from the Kenyan government, now at the controls before check-in is still asked.
At the time of departure, another form must be submitted: the PASSENGER LOCATOR FORM.
This is a form by which contact information and address specifications are collected to allow the Italian Health Authority to contact them promptly if they are exposed to a contagious disease.
In case of travel by air, it will be the carrier's responsibility to verify that the DPLF has been completed before the passenger boards the aircraft.
Failure to complete the form will result in denial of boarding.
For further information, it is recommended to consult the above mentioned Orders, the website of the Ministry of Health and the airlines involved. The dPLF must be sent before boarding. However, the field regarding the seat number assigned on the flight can always be modified.

To fill in the dPLF it is necessary to 
- connect to the website https://app.euplf.eu; 
- follow the guided procedure to access the dPLF; 
- choose Italy as country of destination; 
- register on the site by creating a personal account with user and password (it is necessary to do this only the first time); 
- fill in and send the dPLF following the guided procedure.

Once the form has been sent, the passenger will receive at the e-mail address indicated during registration, the dPLF in pdf and QRcode format that he/she will have to show directly from his/her smartphone at boarding. Alternatively, the passenger can print a copy of the dPLF to show at boarding. It is sufficient to fill out a single dPLF per household. For further information please consult the European Digital Passenger Locator Form website. For detailed information on the compulsory compilation of Passenger Locator Forms please refer to the website of the Ministry of Health.