Okay, so if I control a Krark's Thumb, a Mirror Gallery, a Sculpting Steel that is a copy of Krark's Thumb, and a Goblin Bomb, I get 4 chances to “correctly” flip my coin, correct?

Pretty much. If you would flip a coin, you apply one Thumb, and you would flip two coins. The second Thumb then applies and replaces each one of those flips with flipping two coins each. So flip two, ignore one, then flip two more, ignore one of those, then look at the two flips you didn't ignore and ignore one of those flips.

Essentially, you can flip 4 coins and ignore 3 of the results.