If my Grounded figure has Super strength and is caring an object can he be carried by a Flying character with super strength?

No. From the Danger Room rule book (page 20):

During movement, flying characters, characters with the transporter ability (transporters), and characters using certain feat cards, powers, or team abilities can carry other friendly characters that have the dolphin or boot speed mode. Flying characters, double-base characters, transporters, giant characters, and colossal characters cannot be carried. A character can carry only one character per turn. A character that can carry other friendly characters cannot pick up or carry a character that is holding an object; however, if its abilities allow, a character that can carry other friendly characters may carry both a character and an object.