In The Dark Knight Rises, I've noticed that Tom Hardy/Bane frequently walks and stands while grabbing his coat/shirt. Here are some examples:
Is this stance/pose inspired by specific comics? Or is this purely part of the movie?
It is unlikely that this posture was one inspired by comics since in the comics, Bane is rarely shown wearing a shirt or jacket at all.
I suspect it is a command posture designed to make him appear larger than life, take up more space or to appear more imposing. Most information on the psychology of body language do not cover menacing poses by megalomanical super-villains so I am having to speculate on why he might.
Considering his fighting prowess and techniques, it also gives him the ability to keep his hands at a level optimal for fighting and defending.
Considering the character from Tom Hardy's point of view, it may be a way of making Bane more distinctive from the rest of the rabble that he was leading. A posture of calm menace. Bane rarely carried a firearm and was likely seen more dangerous because of it.
Since Tom did not get the benefit of using his full facial features, the movement of his hands could be used as a means of expanding his emotional/psychological range.
This image may explain it best: Bane considers himself a conqueror and liberator (albeit only for as long as Gotham lasts) and uses such poses as a form of psychological domination or intimidation. You can almost hear them saying "All Hail the Conquering Hero."
As the accepted answer states, he doesn't have anything to grab in the comics, but the choice to have his fingers under his chest plate could be a practical one from Tom Hardy actually having to wear a chest plate.
When you are wearing something heavy on your heaving chest for an extended period of time, it starts to constrict your chest movement and placing your fingers under, either at the sides or near the neck, it helps ease the pressure. Often American Football players adopt a similar stance for comfort on the sidelines from their chest guards, although it is less pronounced as the jerseys allow for little room for motion.
As well crossing your arms or other 'tough guy' stances are hard to take with the chest plate on (crossing your arms looks silly), and by sticking his fingers under the plate, it further puffs out his chest making him more intimidating.
When I was in the army and deployed to Iraq I'd have to wear my body armor for 10-12 hour stretches while out on patrol. With the weight of the plates alone and the extra ammo attached to my vest I would do the same thing to release pressure and let some heat escape.