If a standard-sized character (or giant or colossal for that matter) carries two tiny friends, does he receive a -2 penalty on speed?

Yes they do, the Carry granted by Flight or Transporter symbol always receives the -2 regardless of carrying smaller characters.

This is inaccurate. The first smaller character does not affect your speed, the second causes you to -2.

I do not see what is inaccurate about my statement.
That's not to say that a Flier could not carry only a single Tiny and take no penalty, but that is because they are using the Carry inherent to their Size, not their Flight. I could choose to carry a Tiny Character using flight instead of my inherent size, and take the penalty to my speed if I could find a reason that would benefit me.

It's not inaccurate at all. The innate Carry from Size does not give you a -2 modifier. Any other source of standard Carry does.

In fact, you can choose to Carry a smaller character via a normal Carry ability and give yourself the -2, if you want. Not sure why you would, but you could.

Point being, the size of the character(s) being carried really has nothing to do with it. The Carry ability that you're using at the time is what matters.

The way Azure worded it is confusing, because he didn't ask about flight, he asked about size, that's why I didn't understand what he was talking about. I apologize for calling it inaccurate I suppose it was just oddly and unnecessarily pedantic.

To make it as clear as possible, (because unless they are both tiny it doesn't matter) when carrying a single smaller character, whether you have the wing/transporter symbol or not, you don't -2, when you carry more than one, you do.