Does mysticism fall under religion? 

Depends on how one defines religion and mysticism.

Do chakras fall under astrology is a similar question. 

We discuss the scientific aspects of Religion, and/or how it relates to science.

Religion can be considered a form of mysticism, as they are both faith based, subjective belief systems, lacking any objective evidence.
As such, for the purpose of a science forum, they both fall under the heading of 'MumboJumbo'.

50 minutes ago, JohnPBailey said:

Does mysticism fall under religion? 

No. Religion is the domestication, and later institutionalization of spirituality.

Mysticism is another, more chaotic manifestation of spirituality.