self- here means "able to act on its/their own". Normally what follows "self" is an action that would normally require some outside supervision, input or intervention. It can be used to refer to both people (self-taught) or objects (self-heating).
Young children often have books read to them, or read books with help from parents or teachers. You might see "self-reading" used in this case to mean:
1. A book which has audio, so it "reads itself" to the child.
2. A child learning to read books by themselves without help.
Another meaning of "reading" is "to take a measurement from an instrument". e.g. "a man came to read my electricity meter." If my electricity meter was connected to the internet and sent readings to the company, such that no human intervention was required, we could call that "a self-reading meter".
These terms are not very common, but understandable.