Dogs nibble and bite on blankets and other things to explore them. Dogs explore the world mostly through their senses of smell and taste, which is why puppies are so prone to chewing on things. Teething also causes young dogs to favor chewing as they cut new teeth.
Dogs chew and suck on blankets for a number of reasons. The sensation is soothing on their gums if they have irritated gums or if they are young and teething. The blanket may also have a scent they like. They might also be playing with the blanket, and one form of play is to chew on the item. Picking up a chew toy and directing the dog to it instead of the blanket redirects the behavior. Dogs often mistake blankets as toy obstacles when their owner is in bed. This can be corrected by directing the dog to an actual toy when it goes towards a body part under the blanket so that it recognizes that the blanket movement does not initiate playtime.
Chewing on blankets is a common phenomenon that a lot of dog owners have to work around. Sometimes, the easiest solution is to designate a cheap blanket just for the dog to chew on so that other high-quality items remain unsullied.