Ooooh nice find, I'm so envious...it's celeste!

Don't worry about flats, it's the bike's mechanical soundness that matters.
Check the frame and fork: look for scratches, dents, rust. Run your fingers across the tubes to detect bulges. Visually check for fork and stay alignment. Do the wheels seat straight in the frame and fork.
Is the fork bent?
Check the wheels: spin them in the frame, are they true, are they round? Feel any roughness while spinning? Remove them and spin them in your hands. If the hubs are rough, you can sense it better this way. Inspect the rims. Check for hairline cracks around the nipple holes, and run your fingers along the braking surfaces. Make sure no ridges, dents, etc.
Inspect the drivetrain for wear: how bad is the chain? do the cogs and chainrings look worn out? Test the shift performance of the derailleurs. Check the BB for play.
Bring a few hex keys with you....
Loosen the seatpost and stem/handlebar binders and see if they will rotate free.
Do the same with the brake mounting bolts, and the pedal axles. You are checking for seizure.
Major PITA if they are seized.

If it checks out, or items don't, start bargaining him down.
Nice bike!