Well, no known reindeer species can fly to begin with.

Even though there are 300000 unrecorded species of live organisms (most of them insects and micro-organisms) that does not in any case mean that there is a flying reindeer, which by the looks of
things only Santa Claus has seen.
There are about 2 billion children (under 18 years old) in the world. Since Santa obviously does not visit Muslims, Hinduisms, Jews, and Buddhists, the work load decreases to 15% of the total number, which
is about 378 million. According to the international Population Registration Office there are 3.5 children per house, which gives us a total of 91.8 million households. We can assume that there is at least one
good child per house that deserves to receive a present according to Tradition.

Santa has 31 hours to work, due to the time difference and the rotation of the earth, assuming that he is travelling from east to west (which would make sense, since he's been doing this job for ages). That gives
us 822.6 visits per second. That means that, for every Christian home with one good child, Santa has 1/1000 of a second to park the sled, get off, jump in the chimney, leave presents in everybody's stockings,
leave some more under the Christmas tree, eat his piece of the Christmas pie, climb back out of the chimney, get in the sled and leave for the next household.

Assuming that these 91.8 million visits are equally far away from each other (for simplicity of calculations) that means 0.78 miles per household, a total trip of 75.5 million miles (not counting the
stops to go to the bathroom).

This means that the sled must move with a speed of 650 miles per second, which is 3000 times the speed of sound. Comparatively, the fastest vehicle made by man moves with a speed of only 27.4 miles per second and the average reindeer can run with a speed of at most
15 miles per hour.

Another interesting issue is the load of the sled.

Assuming that each child receives a package that weighs one kilo (two pounds), the sled must carry 321300 tons, not counting Santa, who is said to be fat (even if we don't count the 91.8 million pieces of pie
he has to eat). The average reindeer can carry at most 150 kilos. Even if this infamous flying reindeer could carry 10 times as much, 8 or even 9 reindeers would not in any case be enough. In fact you would need
214200 reindeers. This increases the total weight (not counting the weight of the sled and Santa) to 353300 tons (4 times the weight of the biggest ship ever built). 353000 tons moving with a speed of 650 miles
per second have an enormous air resistance, which causes heat (as a space shuttle re-entering the earth's atmosphere). The first couple of reindeers will consume 14.4 quadrillion Joules of energy per
second, each. In other words it will evaporate instantly with a loud boom, leaving the next couple of reindeers exposed. The entire herd will be evaporated in 4.26 milliseconds. In the meantime, Santa will have
to endure acceleration 17500.06 times greater than the earth's gravity. If he weighs about 100 kilos (which is probably an understatement) he will be splattered to the back of his seat because of the 2107007 of
inertia.

If Santa Claus ever existed, he does not exist any more!