I haven't heard of any parkour classes here but Share3 AlThakafeh in @Shmeisani seems like a good place to do some freestyle self teaching! Or just do some indoor hardcore parkour like in The Office
There's an area where some kids skate and hang out @Shmeisani thaqafa street... you can also probably go to the arehere lots of guys play classical guitar on rainbow street
@Days Inn - Amman. On the traffic light that leads to and from Shmeisani, Wadi Saqra, & Rabieh. I have been there inn Ramadan if I recall correctly, it had both.