In 1943's "Falling Hare" Bugs battles a gremlin at a US Army Air Force base. At one point Bugs is crushed into a disk and the Gremlin threatens to drop him through the bombay doors. Later, as the plane goes into a tailspin, Bugs flattens out and slides off his seat onto the floor. Also in 43, "A Corny Concerto" was Bob Clampett's spoof of Walt Disney's Fantasia. In the first sequence, which had Bugs with Porky Pig and a dog, when Bugs pretends to have been shot he turns green in the face and flattens out.
1948's Haredevil Hare has Bugs launched to the moon. The G Forces of the liftoff flatten him against the side of the ship. He peels himself off to reinflate. (This is the cartoon which introduced the Marvin Martian character)
Also in 1948, "Rabbit Punch" has Bugs in the ring against the Crusher. When Bugs tries a "windmill" maneuver, the Crusher's weight flattens him. Bugs peels himself off Crusher's back.
"Falling Hare" and "Corny Concerto" are in public domain. The others are under copyright.