How am I supposed to know where Zapdos will appear in Platinum. Also, do roamers have encounter slots?
The roamers don't have encounter slots :) They are generated when talking to Oak after beating the Elite Four :) Each bird have a different starting frame. I believe Moltres is on frame 1, so if you want to RNG all three birds, you should start with Moltres.
If you have already released the birds, KO the one you want to RNG, beat the Elite Four again, and then save in front of Oak and start RNGing it :)
Also, if you want to catch the birds, you should lead with a pokemon 1 level below the birds (with mean look) and go in and out of a route and see if it's there. Just repeat until you get it :)