If would be helpful if you said WHEN you plan to go, and how many days you will have (not including arrival or departure days). Also, have you looked at a map? Patmos is waaaay out of the way for the 2 other destinations.... it's the northernmost island of the Dodecanese chain, has no airport, you either must go to Rhodes or Kos (fly or ferry) then ferry North. Or fly to Samos & get ferry (not daily) to Patmos.
Also, how can we tell how many days you should spend in each, if we don't know your interests??? If you just want to look around Chania, browse the city, shop a bit... 2 days. If you want to use it as a base for driving out to ruins or beaches or scenic areas, a lot more. If you're going to Patmos mainly because of the Monastery and the (purported) site of the writing of the Apocalypse, it's a day trip... or are you going for a beach vacation? For Naxos -- there are SO many activities, hiking opportunities, museums, visits to hillside villages, concerts etc... you could easily spend 6 - 10 days and not see it all.
For the best advice, it works best to be very specific about trip timing, length, all destinations, and Why you've chosen them. It's also helpful to give an indication of budget (i.e., planning to have private guides? or a group bus tour? or D-I-Y using guidebooks & your smartphone?) Of course, that would require your doing some research. But then we can address your interests, without having to write everything we know about your wish list.