1: What is Tazkeer and Tazkeer Fi Al-Quran? 2: Is this some particular way of Tafseer or what? 3: Are there any books on this topic?
According to the source I consulted is that Tazkeer means reminder to both muslims and non-muslims.
So Tazkeer fi Al-Quran means a reminder that is stated in the Quran.
You could say there is the Quran about this topic. Because it's full of reminders for muslims to obey.
This might not be an answer as I've said in my comment above that it seems unclear to me what you are referring to and the people who used this term should know it better.
Tazkeer or better Tadhkeer (or tathkeer) تذكير in Arabic means reminder of something.
Tadhkeer fi al-Qur'an التذكير في القرآن from a linguistic perspective might be correct if it refers to a reminder of something in the Qur'an. But one would ask himself a reminder of what? It might refer to verses that remind us about hell or death or jannah or punishment or of Allah in general etc.
Or might be linguistically rather incorrect if it means reminding each other using the Qur'an or helping each other remind parts one memorized from the Qur'an. The later is often used by jama'at a-Da'wa wa tabligh they remind each other of the last 10 surahs of the Qur'an and help each other memorizing the Qur'an: one of them recites and the other verifies the correctness and vice versa.
A better term in this case would be at-Tadhkeer bil Qur'an التذكير بالقرآن especially the linguists of al-Kufa would accept the first version too