When you are considering flow, take an accessory (colorful lamp, throw pillow, rug) that embodies the feel of one room and move it to another room. It shouldn't look out of place.
If that's too restrictive for every room, you can at least use the same neutral repeated in all the rooms. For example, if you choose off-white for the living room, try to avoid bright whites in the next room (unless you are intentionally creating a color scheme with white and off-white).
Flow can also be created with other elements besides color. For example, maybe you use the same style furniture in multiple rooms. Your night stands in the bedroom and your end tables in the living room are interchangeable styles (although maybe not heights for practical reasons).
These two rooms have similar lamp styles and furniture tone, but not great color flow. Since you probably can't see into the bedroom when you're in the living room, I think that's pretty good flow without becoming too matchy. If you're just looking at color though, the bedroom is a little colder and the green and blue a little muddier.

thanks a lot W Brown for your ideas.