I've scored 64.89 in GATE 2019 ME in general category. My CGPA during BE is 8.56. what are my chances to get into IIT and in what field?

As per your gate marks your predicted gate score will be 660-680.

As per your score and previous year cutoff, the colleges you get in first round are:-

IIT Patna Mechanical Engineering Mechatronics

IIT Gandhinagar Mechanical Engineering Mechanical Engineering

IIT Madras Applied Mechanic Biomedical Engineering (Biomedical B.Tech)

To know more about your chances of getting other colleges check out the PSU/college predictor link below:

https://engineering.careers360.com/gate-college-predictor