Do Kenya citizens need a transit visa for Egypt?

If all of the following apply you don’t need a transit visa:

• You are transiting through HBE Alexandria airport

• Your transit time is less than 6 hours

• You don’t leave the transit area to recheck luggage and don’t pass through customs/immigration

If any of the above criteria don’t apply you need a transit visa.

You may not need a transit visa if you will be staying for less than 12 hours and remain at the airport for the duration of your stay. [Soure: Egypt Transit Visa Eligibility & Requirements]

The answer is not clear.

Entering the OP's data into Timatic returns the following:

TWOV (Transit Without Visa):

Visa required, except for Passengers transiting through Alexandria (HBE) with a boarding pass for a flight to a third country within 6 hours. They must stay in the international transit area of the airport and have documents required for the next destination.

Visa required, except for Passengers with a confirmed onward ticket for a flight to a third country within 48 hours. They must have documents required for the next destination.

This TWOV facility does not apply when transiting through Alexandria (HBE).

The first paragraph says TWOV is permitted at HBE under the conditions presented in Daniil's Answer. The third paragraph, however, says TWOV is not permitted at HBE. I don't know how to resolve this.

There's more uncertainty further down in the same Timatic report. The following text appears:

Passport required.

Nationals of Kenya are allowed to enter with an expired passport.

When nationals of Kenya travel with an emergency passport, a national ID card or a temporary passport, it must be valid on arrival.

Passport Exemptions:

• Nationals of Kenya with a national ID card.
• Nationals of Kenya with a machine-readable temporary passport

VISA NOT REQUIRED.

Minors:

• Passport not required for minors registered in the parent/guardian's passport if traveling with the passport owner.
• If minor is traveling on a passport of a parent For details, click here

Warning: - Passports and other travel documents accepted for entry are considered valid until the day before the expiration date.

It's not clear if the capitalized words "VISA NOT REQUIRED" apply to the sentences above (in which case a visa for Kenyans is not required), or if the words apply to the sentences below (in which case Minor travelers don't require a separate visa.

The latter interpretation seems more likely, as the report's previous use of capitalized text — such as "TWOV (Transit Without VISA):" at the top of the Timatic report — must necessarily refer to the text that follows, as there's no text preceeding.

I was unable to find a live web link to the Egyptian Embassy in Kenya.

Given Timatic's uncertainty, the OP should inquire directly of his air carrier for the Italy > Egypt leg what documentation will be required to allow boarding. If the OP is risk-averse, he should apply for an Egyptian visa or transit visa.