Try speed cameras that automatically track those overspeeding and send them tickets. These things have been done elsewhere. Force police men to wear cameras and videos streams...before making an stop or arrest..otherwise it becomes null and void.
It is not possible to put "speed cameras" on every possible road where speeding is possible---even in the Elsewhere, and much less in a place like Kenya. What's more, such a camera does not, even in Elsewhere, mean that a copper cannot stop a speeding person. I don't know how wearing "cameras and videos streams" would help in such a case. What would they show if a copper stopped a speeding car? And, whatever the case, what would stop a copper from claiming that he forgot to turn on his gizmo, or that the batteries had failed, or whatever?
Even with all the cameras (worn and otherwise) rolling, bribes can still be arranged in other ways. As it is, the coppers are already ahead with their "anti-detection methods":
A section of traffic police officers are using touts to collect bribes from motorists in different parts of the country to avoid detection from authorities.
http://www.the-star.co.ke/news/2016/05/30/revealed-traffic-cops-now-use-touts-to-collect-bribes-kavuludi_c1360506The other thing is that in this particular case the notion of using technology to reduce the human element is especially problematic: Every one in the "food chain" is eating, with the lower levels passing a cut to the upper levels. So one can be sure that at all levels there is a vested interest in making sure that the technological approach fails.
To my mind, the best way to deal with corruption is to deal with it harshly and promptly. A place like Singapore has done this successfully, and China has also made great strides. But that requires political will at the highest levels, and that is non-existent in Kenya, where everyone is eating if they can. In Kenya today we have a president who got his wealth from theft; a Deputy President who, among other things, is know As "Arap Mashamba"---and not because he is a good farmer; senators and governors whose wealth is of very questionable origin; .... ; and so on downwards. Who will bell the cat?
Societal attitudes also matter: Kenyans will complain endlessly about corruption, but only when it is to their disadvantage; otherwise they have few issues with the vice and will happily indulge in it---be it the stealing of examinations, the stealing of land from others and bribing the judiciary .... whatever it takes to "get ahead". And on top of that, it is the "successful" criminals who are admired while the honest-but-poor are despised for not grabbing when they can.