First, I am not an expert here, so this is only based on what I've seen others do - some more input or research is probably worth your while. Also this is based on things like pinstripes and flame jobs for cars and motorcycles.
On a good custom flame or pinstripe job, there is no detectable ridge. If there is, it's a sign of a job that's not done to the "peak" of the artform. It may look good to 99% of the public, but hot rodders and custom bike fanatics are a pretty exacting bunch.
First, you need to get as clean a line as possible. Ordinary masking tape has too many irregularities to make this possible. The usual "blue" tape is better, and may be good enough for model rockets, but the bike and car guys use something called fine line striping tape. It's more flexible (good for making curves for those flowing flames!) and has a nice sharp edge and is completely smooth, so paint is less likely to seep underneath like it does with ordinary masking tape. My guess is that drafting tape might make a good substitute for straight line work (e.g. your checkerboard). Whatever tape you use, you'll need to be sure it's not so aggressive as to pull off your base coat.
Use your fingernail, a popsicle stick or some other tool to make sure the edge of the tape defining the border is consistently stuck down. Again, this is to prevent paint bleed underneath the tape.
Shoot the color in very light mist coats. The first should be just a light "fog". Build up only *just* enough to get complete color coverage so no base shows through. If you build any more than this, the paint ridge will be higher and harder to deal with. As soon as the paint is dry to the touch, remove the tape (an xacto is a good tool to use to "pick" up the edge of the tape.)
What you've done to this point is to put down the pattern (stripe, flame, checker) as neatly as possible, doing what you can to minimize bleed and excess build up. A lot of folks may wish to stop here and say it's "good enough".
If you want to go further and get a smooth surface, then more work is required. Shoot a couple of coats of clear finish on top of everything. This will "smooth" the paint ridges to make them less noticeable. Again, many guys will say this is fine and stop here.
Even at this point, however, the paint ridges of the pattern will "telegraph" through the clear - so it's not smooth yet. To got further, you need to wet sand the whole thing using wetted sandpaper. Be careful not to soak the exposed cardboard interior surfaces! Using a flat sanding block, start wet sanding with 400 grit, work up to 600 and then to 1200. Some go to 2000 but that's pretty extreme. Be very, Very, VERY careful not to sand through the pattern layer. It's ok to go trough the clear, but if you burn through the color pattern layer, you'll need to start the over again. What you've now done is sanded the telegraphed "humps" of the clear down to the level the valleys where there was no color pattern. I.e. the paint should be smooth and "flat" and "straight" - as the body guys call it. Also, you'll note that the gloss is completely gone. The sanding has produced a flat surface sheen. Don't panic - what you've done is only supposed to get the surface smooth. If it's not completely smooth, you need to choose between sanding some more - at the risk of burning through the color - or shoot another layer of clear to give you some more "build" to work with. It's more time, but less risky and if you've gotten this far, you've already got some significant time invested so to blow it here would be a shame.
After you've smoothed and wet sanded to your satisfaction (body guys take days, even weeks on this step). You can shoot on a final clear coat to give it a good shine and restore the "depth" lost during the wet sanding process (BTW, body guys call this process "color sanding").
99% of car body guys would stop here. If done right, it looks pretty darn good at this point and the paint finish from all volume car mfrs consider it done once the final clear coat dries. Even your basic Chevy looks pretty darn good at this point.
The other 1% who are going for that perfect concours finish would sand once again to remove the slight orange peel finish that is inevitable with even the best spray equipment, and then use power buffing equipment to polish the paint to its final gloss. That gives you an idea of how fanatical the show car crowd is.
Now, who's crazy enough to do the "whole" works for a cardboard model rocket? Though it's not me, I bet someone out there is!
