The new Italian Prime Ministerial Decree of 16 January has not in fact changed anything as regards travel beyond Europe, i.e. the so-called 'Schengen area'.
Thus, travel for tourism remains officially prohibited.
Those who have a second home in Kenya or a regular rental contract or have proven reasons of urgency can demonstrate this with self-certification and attached documents and embark, subject to an online visa issued by the Kenyan authorities.
By order of the Kenyan Immigration authorities to the airlines, in fact, those who do not have the online visa will not even be boarded on a flight to Kenya. We would like to remind you that in order to fill out the online visa you need to go to the accounts.ecitizen.go.ke/register/visitor link on the Kenyan immigration website. The visa is valid for 3 months from the moment it is issued (and not from when you arrive in Kenya) and can be extended by another 3 months.
The fact that many Kenyans are leaving for tourism anyway and are not checked at the airport does not mean that they are guaranteed to be able to board the plane. Sometimes random checks are carried out, sometimes a fussy employee at the check-in can make you lose your trip and your ticket.
Then there is the "necessaire" chapter for the pandemic emergency: 

TAMPON: To enter Kenya you must present at the airport in Nairobi or Mombasa the PCR swab (not serological, not other type of analysis) carried out no more than 96 before departure. This is what the Kenyan protocol states and is also reported by our Ministry of Foreign Affairs. However, lately it may happen that there are indications of 96 hours before arrival in Kenya. This has already happened and it is a problem of interpretation of the protocol (which in English says "before travel"). To be totally sure of entering Kenya, it is therefore advisable to have the Tampon carried out no more than 96 hours after arrival in Kenya.
WITH THESE REQUIREMENTS THERE WILL BE NO NEED FOR QUARANTINE
QR CODE: You need to obtain the QR code that will be scanned by the Kenyan authorities to alert the Ministry of Health and other offices of your presence in Kenya. You can get it by filling in and sending this FORM: https://ears.health.go.ke/airline_registration/

To return from Kenya, the Kenyan government does not currently require a swab, nor does Italy require one on entry (and doing so does not remove you from quarantine, which is still subject to occasional checks or your communication to the ASL). 
For the moment, the obligation to have a swab when returning to Italy can only be requested by airlines.
It is therefore advisable to ask the airlines with which you are travelling and, in any case, it may be a form of respect for other travellers and peace of mind for those leaving.