When a dog licks their feet constantly then it could be a sign of the dog having anxiety, the dog could be nervous, dry skin, flea allergies or other allergies.
Your dog may also have something in it's paw that they are trying to get out especially if you also notice the dog is also trying to bite at their paw while they continue licking the paw.
Some paw licking or dog feet licking is normal behavior as they use their tongue to clean the paw but excessive paw licking is caused by something that is wrong with your dog.
Check the dogs paw for any splinters or something that could be in the paw and also check for any sores that the dog may have on it's paw.
The dog may also just be licking it's paws because the dog is bored.
If you think something is wrong and the dog continues to lick his paws or paw constantly for more than a few days then you might want to call a vet and have the vet check the dog out.