Is it sunnah of Prophet Muhammad (peace be upon him) to clean one's plate after eating by licking it with fingers or tongue?
Yes, it's sunnah.
Hadhrat Jabir Radhiallahu ta'ala 'anhu reported:
I heard from Rasulullah Sallallahu 'Alahihi wasallam that The Satan is present with any one of you in everything he does; he is present even when he eats food; so if any one of you drops a mouthful he should remove away anything filthy on it and eat it and not leave for the devil; and when he finishes (food) he should lick his fingers, for he does not know in what portion of his food the blessing lies
And That's why it is sunnah to clean the plate as you don't know in what portion of your food has the Barakah.