The sentence is grammatically ambiguous. It could mean A. Reason born of experience, and knowledge born of experience OR B. Knowledge born of experience, and also reason. To me, B makes more sense in context. Reason is the simple application of logical rules, and does not require experience. Knowledge requires experience. Most modern philosophers would say that logic and experience are the only two possible ways to discover truth. However, the author is saying that instinct is stronger than both of them.

I agree with Chris. I'll phrase it a little differently. The statement is ambiguous. It could mean A) instinct (which was stronger than reason and knowledge) [alone] told her that ..., or B) instinct (which was stronger than reason) and knowledge (which was born of experience) [both] told her that ... More context would clarify the intended meaning. Meaning A is my choice (emotion is stronger than reason and knowledge) As for the qualifier "born of experience," in my opinion it modifies knowledge. There is a famous saying "Good judgement comes from experience. Experience comes from bad judgement."

Instinct (adjectival phrase) and knowledge (adjectival phrase) told her that ...