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So, let's say I have a Regieleki with a maxed out speed stat, holding a Choice Scarf, +6 in speed, having Tailwind active, and skill swap Swift Swim onto it in the rain. How fast would Regieleki be exactly?

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Turn-order wise, this Regieleki would be treated as having a speed stat of 1808. If its teammate had 1810 speed, it would be slower than that, but faster than an opponent with 1807.

The trick is that the game forces a couple speed limits. 10,000 is the value of the hard cap, where no matter what the normal formula for stats would dictate, anything that would be greater than 10000 gets stopped at that point and refuses to go any higher. (This is because of the current implementation of Trick Room, which replaces all speeds with (10000 - speed) if it's present, and needs to make sure it's never subtracting anything big enough to produce a negative number as a result.) That then gives way to a second cleaning system, this one more of a pit trap: any speed stat that's 8192 or higher gets dropped backward by subtracting 8192, so speeds that were fast enough to slam into that first wall will also be pushed back by this, and 1808 is the point it lands on.

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Yay I love math

Let's see here... First you add the Choice Scarf boost to 548.

548 x 1.5 = 822

Every +1 stat boost in Pokemon is equivalent to 50%, so a +6 Speed would be a 300% boost, or x4.

822 x 4 = 3288

3288 x 2 = 6576

And then, finally, 6576 x 2 = 13152

Too Much Math;Didn't Read: The answer to your question is Regieleki would hit 13152 Speed

Regieleki is S P E E D