Are the feet red, swollen, or crusty/flaky?
This could be indicative of a local irritant (such as deicer) or inflammation/infection from bacterial, fungal and/or parasitic sources. Even if the inciting cause is no longer present, constant licking and chewing can become a self-propagating cycle of continued trauma to the skin and continued inflammation.
Is licking present in the absence of any noticeable pathology of the feet or toes?
This could be from inhalant allergies causing general itchiness, arthritis or other painful "interior" conditions causing pain in the area without visible infection, etc. on the foot.
Are there any irregular lumps or bumps deep between the toes or foot pads?
Cysts or other growths or small abscesses can occur, causing discomfort and licking.
My dog is just licking without any visible signs of something wrong on the foot!
Foot licking can be simply a habit behavior as well; seen when the dog is relaxing, stressed, or bored. Some dogs even chew at their nails with this type of behavior.
Depending on what your veterinarian finds on examination, treatment to stop this behavior will be aimed at the underlying cause. For cases of allergy or infection, there are medications and/or dietary changes that can be made to assist with the problem. In situations where pain is the underlying cause, that should be dealt with directly to alleviate the licking. Growths or abscesses are usually treated surgically. Pet owners should always be vigilant about environmental hazards to feet; such as deicing compounds in the winter and very hot pavement tar in the summer.
Behavioral modification to stop paw licking and chewing, like any behavioral modification, takes time, patience and consistency. There are several topical products that can be used to discourage this behavior (bitter, hot taste, etc.). Physical restraint, such as an e-collar is often used for medical conditions to allow the foot or paw to heal and thus take away the inciting cause to lick. Distraction is also a good technique: playing games, offering other toys and incentives to keep your dog occupied coupled with positive reinforcement will help break the cycle. If additional behavior help is needed, consider working with a
specialist in veterinary behavior