The inertia starter from a 1928 biplane. Everybody has one of these lying around, right? Check your backyard.
An airjet from a dentist's office. Next time you go in to get a filling, just whip out your smartphone and record that sucker (pun intended).
The sound of an arc light motor stopping and starting. I'll confess: I'm not sure exactly sure what Burtt is referring to, but it's possible he's talking about a motor used to generate an electrical current for an arc lamp? While arc lighting is still in use, the equipment he's recording here probably dates back to earlier in the 20th century. So you might need a time machine to find a working one—but once you've got that, it's a piece of cake.
Tank turret motors. I'm sure the army would be thrilled to let you come in and record some audio.
Rattling water pipes from inside Lucasfilm's office, circa 1980. Just tell them you're on a field trip to collect all the sounds for the Falcon's hyperdrive. Let 'em know we sent you.