What is Ben Affleck's character doing massaging his leg with a wooden stick

In the beginning of the movie his father says to the therapist something along these lines:

"If he's vulnerable to loud noises and bright light he needs more of it, and not less, as the world is not a controlled environment"

So it is some kind of self-disciplined training to make him more resistant to stimuli from the big and scary world, to train him in remaining calm in stressful situations.

And I think the rolling on his shins is not really massaging, but to make his shins stronger/less painful in fights (opinions on the effect of this may vary, some say it only deadens your nerves, others say it increases bone strength as well). If you roll hard enough, this is everything but comfortable and adds to the stressful situation. CS Interview: The Accountant Director Gavin O’Connor

He only does this flashing/loud music training in his house, outside in the world, outside his comfort zone. Inside his trailer he can relax, he feels safe there, and he can listen to classical music and let down his guard.

It's a textbook Muay Thai technique called shin conditioning. He is using a rolling pin which is very common in the martial art. Remember that his father had him trained in many martial arts and especially that the Asian analysts told the girl agent on the phone that hooded figure in the survalence tape at the beginning killed the mobster with one kick to the head which lead to "blunt force trauma"...I can't believe no one else understood this...but anyhow it makes it all the more awesome.

Very true. If you administer enough pressure it causes tiny fractures in the bones which in turn rebuilds themselves refilling the fractures creating a stronger less breakable bone. Some arts call it Iron (whatever the body part inserted here).

Muay Thai is a great example, but it not only works on the shin. The version portrayed in the movie also works with other bones, but there are many other ways to condition many of the other bones in the body. Finding a sifu to instruct you in the correct way is the correct way to go about Iron Body, not an actor on a movie. I do not recommend trying this at home without correct supervision. Also, anyone can hurt another, those truly gifted can also heal those who are hurt. Seek peace in any interaction, but remember your abilities in the nonpeaceful ones!

Because the accountant is Autistic, his father put him into an overstimulated place with the loud music and flashing lights, then taught him how to deal with the over stimulation by doing the shin thing and using the nursery rhyme muttering. His dad tried to make them tolerate more than the usual because he knew the autistic boy would suffer bullying. I have an autistic cousin who does the slf stimulation and nursery rhyme to find a calm place. Often Drs want to drug them, when sometimes they need to deal with life, but find a self soothing technique.

The technique used is calming because it essentially serves as an effective method to interrupt an over stimulated state of anxiety or stress. The loud music serves as an auditory interrupt. The flashing lights serve as a visual interrupt. And rolling on his shins serves as physical interrupt.

The rolling part ties into the stimulus. It’s painful and plays some role with the lights and music.

Highly doubt he’s worried about leg day while completely shooting his anxiety to the moon.