It is not necessary to increase water intake while off creatine. The creatine will flush out of your system naturally. You'll go back to baseline after a few days.
Also, while not part of the question, I'm not sure the point in cycling creatine at such rapid intervals. Some people like to cycle off it for a couple weeks every six months or so, but I've never seen anybody suggest a three week cycling schedule. Your muscles would never reach full saturation unless you load it the first week of each cycle.
To me, it sounds like you are over-thinking it. Just take 5g or so a day. If you get thirsty then drink more. If you're not thirsty, then you're likely already drinking enough.
EDIT:
According to this study that Thomas Markov posted, it can take as long as 30 days for creatine to completely leave the system, so that seems to indicate cycling this rapidly will not be useful.