Just like in glass work...... you want the COEs to match up pretty closely.
Firing shrinkage and COE are not related in clay bodies.
To figure glaze COEs you can use glaze chemistry software to reasonably accurately predict them.
No one has yet figured out how to model the complex activities of clay bodies. COEs on clay bodies are measured... using something called a dilatometer. Dilatometers are the province of industrial ceramics labs. You can do glaze with a dialatometer too .....a little more difficult.
There is a "quick and dirty" way to establish a clay body's COE. You mix up a set of testing glazes that have steadily increasing COEs. Then glaze some test tiles with the glazes... and the one in the center of the "shivering on one end and crazing on the other" curve is close to the actual COE.
Professor of Ceramics; New Hampshire Insitute of Art
Guest Professor, Wuxi Institute of Arts and Science, Yixing, China
Former President and Past President; Potters Council