Incorporating martial arts and freerunning/parkour?

Okay so this kid, Greg Townley:

is an impressive tumbler, he is also seen doing martial arts and freerunning/parkour throughout the video.

Does Coach Sommer implement martial arts training and/or freerunning and parkour in his training sessions with his students?

He was instructed by Damien Walters:

who is also a proficient and expert tumbler. His showreel also has him demonstrating some martial arts and freerunning as well. According to the freerunning wiki, he is a " a professional stuntman, gymnastics coach and free runner."

http://www.streetstunts.net/wiki/Damien_Walters

His videos on youtube have garnered over 30,000,000 views and has over 90,000 subscribers, so he is quite well known.

No Coach does not implement martial arts or parkour in his training, but some of his kids enjoy practicing it on their own

I don't know how coach trains his kids but from a sports perspective it just wouldn't make very much sense. Number one thing to get good at a sport is to practice that sport, especially one that requires such a variety of skills like gymanstics. It basically comes down to training time, if you have time to practice martial arts during practice why aren't you practicing skills which directly relate to your sport.

However, when I did tumbling I would always stay after practice and work on things that they don't normally teach in tumbling like gainers, different kicks, double legs, wall flips and so on.

That kid is one good tumbler, I don't think I've seen too many kids his age doing double layouts.