Places to learn Parkour
There are a number of parkour groups in India. Though it is not that popular or widely recognized in India, some of the people in the scene are really good. Parkour Mumbai and Chennai Parkour are definitely worth mentioning. Also, there are parkour communities in Hyderabad, Chennai, Calcutta, Odisha, Nashik (these guys are good), Delhi, Bangalore (Chaos Faktory), and Assam (AsPK).
I used to practice with the Calcutta chapter (Parkour, FreeRunning, Kolkata(also Parkour Bengal)) but had to stop practising because of my current job which is in Pune. I was also lucky enough to train with the guys from Chennai, and they're really good at what they do (primarily because they have their basics right and pack in a lot of strength training, endurance training, and conditioning.) The session with them left me in pain for 2 days, but the exercises also helped me become stronger and helped me in correcting some of my moves which had flawed techniques.
You can also check out the website for Indian parkour. These guys are very active on facebook and are willing to help out.
If you don't live in any of the aforementioned cities, you can always start practising on your own. You can follow Parkour Generations, American Parkour, 3Run, Parkour Generations Asia. Their lessons are really helpful and will help you in getting your basics right and their posts will also help you in understanding the philosophies and the principles behind this wonderful sport.
P.S. Word to the wise, DO NOT try the advanced moves without proper training and conditioning. You might end up injuring yourself (maybe very seriously). Hope this helps. And all the best.
Edit: Like Prabhu Mani has mentioned in his answer, Parkour Circle is another group in Chennai you can train with. In Pune you have MYOW who train in Bund Garden. I train in Kothrud with my own crew. I'm also planning on training with MYOW to improve my skills. Feel free to drop by anytime.