You can find unique looking book all over the world that increases Chiyo's magical knowledge when you interact with them while she is in your party. The locations of the books can be found in the walkthrough, simply search for the word "Magic book"and you should find them.
how much knowledge we need?
The hexagon in the Yang Tower requires 50, the barrier in the Skylow Tower 40 magical knowledge.
how to get to golden license after finish " magic license "
You start it by talking to Chiyo at the sleeping chambers. It requires Chiyo to be level 25+ and that you have constructed the big farm in Central from the overview map. (The farm where you can release monstergirls)
Then you're missing a previous event with Chiyo. Did you have the events about gathering materials with her for alchemy? Did you advance the main story and have Varea at your castle or helped her in the events with Amagal?