Smeargle can learn every move through sketch except Chatter and Struggle.
So therefore, it can sketch revenge.
You can also check this by using smeargle in Showdown’s Gen 7 team builder. Since it’s “legal” to have revenge, it can learn it.
How to Sketch Revenge
Since revenge is a low priority move, you’ll have to wait until the turn after the Pokémon uses revenge, then sketch it. Make sure that you’re faster than the opposing Pokémon. Since you can target your teammate in double battles, the easiest way is probably to enter a double battle with a fast smeargle and a Pokémon that knows counter, protect smeargle and use counter, then sketch your teammate next turn.
Hope I helped!