Questions: what book are you referring to?
Is there a pic of this pattern?
Isn't a kaleidoscope block done with triangles?
This process is very close to Bethany Reynold's Stack n Whack system or even the One Block Wonder, that is layering the fabric to keep the repeat pattern the same on each folded piece.....I guess it will work with any piece of a block one would like to be identical in each block.