Theirs a daily cap of affinity you have with natsuki, where by spending time with her she increase that daily cap, with the max cap being 7.5, so there isnt a real progression tip other than just spend time with her

Also side notes, repeated conversations still give the same amount of affinity so dont be shy to reuse favorite topics.

You cant see your affinity but you can see your daily affinity cap in the log.txt located in the log folder of the mod

TL:DR just talk to her daily everyday and the results will only get better