Can members of the corps carry flying characters?

No the Green Lantern TA only allows a character to carry up to 8 freindly characters. Other than that Figures with the Green lantern TA have to follow the same rules as other fliers which include Flyers cannot carry Fliers.

Actually it's not just fliers who can't carry fliers. Transporters can't carry fliers either. Unless they have earthbound. But then they aren't fliers at that point.

Thanks. I just needed some clarification on that

One more thing. If I have a wild card character using the GL TA and they are not a flyer, can they still copy that TA?

They can copy it all they want, but they cannot use it, as they cannot carry figures.
And no, it doesn't work with the Passenger feat either, as the card specifies that a single character may be carried.
It would theoretically work with a non-flying transporter though, but of course there aren't any transporters who can utilize the TA at present.

Thunderbolts would allow for black knight to carry 8 people.

Yes but he's a flier. The other poster was taking about non flying transporters like Lockjaw but there are no WC or Avengers non flying transporters that would be able to copy GL TA.

I am well aware of the possibilities of Thunderbolting GL TA. Just check out this thread from last summer:
http://www.hcrealms.com/forum/showthread.php?t=137470

And please note that that particular trick doesn't work too well - I was a bit too eager...

Universe Starter Wasp has always been my favorite GL reservist.