The Medway is for most of it's stretch a very coloured river, so you probably only want to fish after a dry period with flies.
I think you'll find though there are clubs who hold the upper stretches which could be productive and clearer. For example
http://www.rtwas.co.uk/
I fish one of the Medways tributaries, the Teise. Whilst the stretch I fish has had all the Pike removed. Right down the end of our last beat I spooked a large pike in the shallows.
The Teise definitely runs pretty clear when there is limited rainfall. So the mixed waters of the RTWAS will definitely hold Pike. Other clubs on the main river are Maidstone Victory and Tonbridge. Although there are many other clubs from all over who own stretches.
If you phone the secretaries of those three clubs I am sure they would be only to keen to help.