Coverdell/529 accounts have nothing to do with the gif tax requirement. Besides, based on the contribution limits to a Coverdell/529 account, even if it did count for gift tax reporting (it does not, never has, and never will) you're not going to come anywhere even close to the $15K maximum you can gift a person without having to report it on IRS Form 709 - Gift Tax Return.
As for the transfer/conversion you did from Company B, you *will* receive a 1099-Q for that withdrawal. In TurboTax you will enter the 1099-Q *exactly* as printed. Then on follow up screens you just indicate that you "rolled it" to another Coverdell/529 account, and that will negate any taxes and/or penalties.
