Thanks for the additional information. It is helpful. Usually when the hair starts turning reddish brown it is due to an enzyme that is contained in a dog's saliva and tears. This is why many smaller dogs have such bad stains under the eyes. There are many products on the market to remove this. They are marketed as Dog tear Stain Removers. The following site has a good chart that discusses these.
The website below has a different approach suggesting altering your dog's pH levels to prevent the staining which you may wish to look at.
There is also an antibiotic that your vet can prescribe called Tylan that has been shown to be useful to stop tears and saliva from discoloring a dog’s coat. You will want to ask your vet about this.
Typically the rash and flaking are the result of an allergy condition. Determining what she is allergic to may be quite difficult to do, but it is likely to help stop the excessive licking of the paws and vulva as well since those are also symptoms of an allergy condition. You should look for those things that changed just prior to her starting either the licking of the paws or the rash appearing. Think about foods, treats, cleaning supplies, laundry detergent, etc. Any of those things might be to blame. Given that it seems lower on your dog, it might be a contact allergy meaning her lower half is coming into contact with the item she is allergic to. It might even be grass or weeds especially if she came from a different part of the country where the vegetation might be different.
She is pretty old so many people would not find it cost effective to do allergy testing though that is the fastest way of determining the cause and avoiding the allergen. While benadryl at 1mg per pound every 8 hours is often effective for some dogs, it is treating the symptoms. You might ask your vet about atopica. It is often used to treat allergic conditions. Read more on it here:
When shampooing be sure to lather well and let it sit on the skin for 10-15 minutes if possible before relathering and rinsing. This gives the shampoo the opportunity to work. If possible dry the hair with a hair dryer on a low setting. Water trapped against the skin can lead to a yeast dermatitis as well which will continue the cycle of scratching or licking even after the allergen is eliminated.
These suggestions should help with the various problems she is having.
I hope this information is helpful to you. If you would like any additional information or have more questions please don’t hesitate to press the reply to expert or continue conversation button so I can address any issues you still have .