You need an ETA for Kenya if you have a Solomon Islands passport

Travelers must obtain an Electronic Travel Authorization (eTA) to visit Kenya for Tourism. Travelers can submit the eTA application online. Once the application is approved, travelers receive their eTA confirmation electronically. A valid eTA is required to board the flight. If the eTA is expired or doesn’t match the traveler’s passport information, travelers will not be able to board their flight. The Kenya eTA is only valid for a single entry, except for in cases where travelers are visiting Burundi, Democratic Republic of Congo, Rwanda, South Sudan, Tanzania, or Uganda immediately after visiting Kenya, do not visit any other countries before returning to Kenya, and their Kenyan eTA is still valid upon return. Travelers fulfilling those conditions can use their eTA to return to Kenya.