The following sentence caught my eye:
However, the Constitution prescribes a minimum level of payments that must be made through Consolidated Fund Services (CFS). (Kwame Owino, Why the State Can't Afford to Give Every Kenyan Money)
To be blunt, the Constitution doesn't prescribe any such thing. The following are the payments which are a charge on the Consolidated Fund established under Article 206 of the Constitution: the remuneration and benefits of the President and Deputy President (Art. 151), the remuneration and benefits payable to or in respect of judges (Art. 160), the expenditure of the judiciary (Art. 173), the public debt (Art. 214), and the remuneration and benefits payable to a commissioner or holder of an independent office (Art. 250).
In respect of any minimum payments to be made in accordance with the Constitution, presumably as a charge on the Consolidated Fund, though the Constitution is silent on this, this would be the "at least fifteen per cent" allocated to county governments out of all the revenue collected by the national government under Article 203(2) and the half a per cent paid into the Equalisation Fund established by Article 204(1).
Consolidated Fund Services, CFS, does not exist, either in the Constitution or in the Public Finance Management Act (No. 18 of 2012), the principal statute on the management of the Consolidated Fund. It is an accounting term relied on by the National Treasury to make payments the payments required to be made as charges on the Consolidated Fund. In other words, it is a line item in the National Treasury's books of account. Consolidated Fund Services encompasses all the payments that are a charge on the Consolidated Fund, that must be paid and are ordinarily not subject to the appropriations processes of the National Assembly.
In short, the Constitution does not prescribe a minimum level of payments that must be made through Consolidated Fund Services. It simply prescribes what are charges on the Consolidated Fund.