I don't think so. The two tires on the same axle should vary by no more than 3% difference in circumference, so you may need to buy two tires. Differences between front and back should not matter.
So if your current tire (the one on the same axle that isn't flat) doesn't have a lot of miles on it, you might get away with just one tire, if you can match the size and tread type. It would be great if you could buy the exact same tire, brand, tread, etc.