When something is "flush with/against" something else, it shows that the two things are precisely aligned. I would also say that I have never heard of someone's head being flush against a pillow before because this term is usually for two inanimate objects. Another example for this sentence could be: - "His head was resting on the pillow" Other example for the phrase could be: - "The table was flush against the wall"

The term "flush with" or "flush against" means "level with" or "even with," in the sense that an object is perfectly aligned with something else (usually another surface that it is touching). If the back of a chair is "flush against the wall," then it stands vertically at the same angle as the wall, so that there is little or no space between the back of the chair and the wall surface. The word is normally used for flat surfaces. In this context, the author seems to be trying to show how firmly Morrie's head is pressed against the pillow, leaving no space in between. (Edited to add: Adam explained it well, I just didn't see his answer until after I'd already sent mine!)