Is there any counter to incendiary shotgun rounds?

Solution 1:

The only real counter measure you can take against fire rounds is to play as an Armored Division soldier and rank the division up to level 3. At level 3, you take less fire damage.

In game, this is denoted by a flame icon in the middle of your screen. When you are on fire, this icon will appear, indicating that your less fire damage perk is kicking in.

Besides that, it's a matter of being able to take out your opposition faster than they can shoot you. Also note that keeping your distance as pointed out in the comments is a good idea, since these rounds are shot from shotguns only, which have a short range.