The most common cause for dogs chewing their paws is that there is an irritation or pain there. Paws (in particular fluffy paws) are prone to picking up debris (thorns,twigs etc) when on walks. This can cause irritation and pain to your dog, and they may be trying to remove the irritation by chewing on their paw.
A wonderful young black and white dog who has been chewing its paws
Another cause could be fleas or red mange. Red mange is a mite that affects dogs paws and can make them very itchy. Another reason for perpetual paw chewing could be stress or anxiousness.