Some riding conditions are going to be extremely dusty, no matter what you do. With the airbox inlet back by the rear tire, and the trapped environment of having a pannier to the outside of the inlet, your options are somewhat limited.
I opened up the top of the airbox beneath the seat, which seems to have helped in that the air inlet is further forward of the dust / dirt churning around the rear wheel, and installed a deflector cover for the rear shock, which seems to help cut down some of the dirt coming forward. I also fashioned some panels out of some cheap flat automotive mudflaps that I tie strapped to the frame behind the side panels, which hang a little lower than the side panels.
Some people use the twin-air filters, which are relatively inexpensive, and carry an oiled spare sealed in a heavy duty freezer baggie.
You might also consider leaving the right side panel at home if you are traveling in extreme dust conditions. Might look a little ugly, but you can get to the air filter a lot quicker and don't have to pull the pannier off unless you have them mounted too far forward for access to the filter cover.
Leaving the left side panel at home leaves you quicker access to the battery as well. The KLR isn't going to win any beauty contests anyway...