Are you talking about picking up SR 20 at Kettle Falls and then heading west? If so, from there to Rockport will take you about 4 days unless you climb more than one pass a day. From Kettle Falls, you start up Sherman Pass (the highest paved road in WA) and descend into Republic. From Republic, you climb Waucunda (sp?) Pass and descend into Tonasket. From there, it's maybe 30 miles to Okanogan, where you then go up and over Loup Loup Pass, down to Twisp and then to Winthrop. (Loup Loup has some 8% grade sections going E-W.) That day is probably 70 or so miles. From Winthrop, it's about 16 miles gently up hill to Mazama, where you start to climb to Washington and Rainy Passes, which is another 16 or so miles. (You reach Washington Pass, descend for about 3.5 miles, and then climb about 1.5 miles up to Rainy. Then you have a long (about 30 miles) mostly down hill ride to Colonial Creek Campground, where you encounter two shorter climbs and descents that take you to Newhalem. From Newhalem to Rockport is easy. That whole days is probably around 90 or so miles, if not more.

I have done basically the reverse twice. Stayed in Rockport, Colonial Creek, Winthrop, Tonasket and Colville, which is a few miles east of Kettle Falls. If you do go this way, I recommend getting the map section of Adventire Cycling's Northern Tier that covers this section. Between Tonasket and Okanogan it gets you off busy SR 20/U.S.97 for most of the way. (You basically stay on the east side of the river and ride through reservation land.) I am almost certain I have mine at home and could share it with you. If you can pull high miles each day, maybe you can shorten things or at least even out the mileages.

Cannot comment definitively on the potential for bad weather as I did my rides at the end of May, but I have to imagine that snow is quite possible. On WADOT's web site there is historical information on the closing dates of the North Cascades Highway that might give you an idea. If you do go, watch the forecast closely. I would not want to get stuck crossing the NCH in a storm. IIRC, except for one U.S.F.S. campground on the ascent to Washington Pass, there are ain't nothing between Mazama and Colonial Creek Campground. The first commercial enterprise you will encounter is a small store in Newhalem, where there is also a U.S.F.S. campground. Next services are at Marblemount. Between Newhalem and Marblemount, the ACA route ditches SR 20 for quieter (and I thinkl flatter) backroads.

Republic has a decent fairgrounds where you can camp for cheap. If the set up is still the same as when I was there many moons ago, there are hot showers and flush toiltettes. (You can find the place on the web.) In Tonasket, I camped on the lawn behind Shannon's Cafe. There were not facilities, but there is a truck stop a half block away with showers, etc. There is a nice KOA in Winthrop. The owners back them gave diso****s to cyclists. Howard Miller Steelhead Park in Rockport is really nice. There are Adirondak shelters you can stay in if the weather is bad. (Call ahead for availability.)