On average, how long would it take for a reasonably new set of tires to develop flat spots from sitting too long?
That depends. The lower the tires Speed Rating for example the less likely it is for the tires to develop flat spots. For tires with higher Speed Ratings Mercedes for example recommends removing them from the vehicle or putting the vehicle up on jackstands if it is going to remain stationary for more than 2 weeks to avoid flat spots.
Modern tires do not get flat spots on their own. The only way to cause a flat spot is through long distance braking at high speeds or under extremely heavy loads. But a stationary vehicle is unable to get a flat spot on it's own. Even on a hot surface, it would require temperatures of up to 300 degrees F to melt certain tires and cause a permanent change in their shape. So we are looking at factors which do not occur in your garage or back yard.
Radial tires don't get flat spots. The old Bias ply tires did, but you don't see those tires around anymore.
