How Do I Treat My Dog For Chigger Bites?

First you got to understand what chiggers are. I recommend doing some research cause lots of people base solutions on myths.

First you need to understand that you usually don't show signs of a chigger bite till after they have left your body. They don't burrow as most believe and swear. They latch on like a Tick, inject a stem into your skin, and inject a enzyme that hardens the tissue. Then they inject the more delicate feeding stem which secretes another enzyme in which liquefies small amounts of tissue for feeding. Chiggers are designed to feed on animals more so than humans and in most cases I seen animals show no signs of itching. The enzymes are more designed to go undetected in animals.

Chiggers last for about 4 days ( they are in larval stage when feeding on tissue ) and they then morph into a adult stage with a strictly herbivorous diet. By the time you show signs of chigger bites they are said and gone.

At that point its totally useless for you to go about a regimen to attempt to destroy them. Just focus on treating the wounds. Wash with a antibacterial soap and follow up with a Benedryl creme afterwords. Thats all you need. There is no instant ailment so don't go through the daunting task figuring out which one works best for you. It will last for about 2-3 weeks, all you can do is keep the wound from getting infected and keep some cream on it to stop from itching.
After going out into the woods or a tall grassy field I recommend washing first thing ( or just stay away from those areas ) with a mix of epsom salt and dish soap. Like fleas and other mites dish soap will kill the chiggers before they can do much damage.

If you find that it is spreading after you wash you either don't have chiggers or you forgot about your sneakers and clothing as well as anything you came into contact with. It all needs to be washed one way or another.

Chiggers will not complete metamorph without a host. Therefor any larva lingering around your shoes or car seats will take advantage of you in do time.
I live in Delaware, its the worst state for mites like chiggers as well as fleas. I also happen to do field work for a Herpetology dept. I know chiggers pretty well by now.

First, use hot water and soap to wash the area. Try to apply rubbing alcohol also to the infected area. Use a wash rag if possible to try and do the final removal of the chiggers. Remember these are tiny bugs.

For relief, you can apply some hydrocortisone cream. If your dog's hair is long, consider trimming the hair to make things easier.

It will take a week or so for the bites to heal.

We have a Boxer who is itching/scratching. There are no fleas. The areas  most affected seems to be groin and neck. We have tried bathing (with a medicated shampoo for dogs, hydrocortisone spray on the reddened areas, Benadryl and Prednisone orally). We believe he is having a problem with chiggers since the other dog does not seem to have a problem. What do you reccommend?

You can't be sure if the problem is chiggers or sarcoptic manage. It is best advised to have a Vet determine the source of the itching. Both chiggers and mites will cause intense itching. Treatment may be very similar. Bathing the dog ( or cat) would be my first recommendation.
There are several treatments which are readily available for mites. Inexpensive and will cure the problem. Don't try to guess what the problem is..in the long run it could end up costing you  much more money.
In locating an affordable Vet,I have found that city Vets are usually much more expensive than country vets. If you live in an area where Vet care is extraordinarily expensive, find a distant vet, usually an older Vet who is toward the end of his career will be more experienced and less apt to overcharge for what should be a minor medical visit. Look in the paper and find one of those breeders who adverstise heavily ( puppy mills breeders) and they usually know the most reasonable vets in the area.