Yeah my lad lives in Rochester, so I always come via the airport route. Although I quite like where Rochester Station is now so sometimes go via train, nice and central, dependent on mood and weather really.
So either park at his or catch the train in.
I just avoid Chatham altogether. If I was to go there, I use to look for parking round by where the old Debenhams use to be in the High St - although as you turn in I would try the car parks on the left first, because it's more central, Primark'ish/Pentagon.
Then when leaving go back towards Rochester direction, avoid the road that drags right down to Brompton, because of those bus lanes. The layout might have changed, so I'm hesitant to say one way. I really haven't a clue anymore lol.