Consider that sometimes large corporations stage big-time giveaways, and there's nothing fishy about that at all. While you might think a million dollars in giveaways is a net loss, it might not be. These companies make billions annually, and sometimes give away cards and whatnot in order to promote new product lines. McDonald's also uses a feeling of scarcity; people love the McRib, but McD's doesn't offer it every day of the year specifically because they want to make people feel it's 'special'.
That having been said, of course this was a scam. First off, the size of the gift card was suspect no matter what - BK would be a lot more likely to give away $5 cards if any. Payment for followers doesn't seem to be specifically against the Twitter TOS but it should have also raised flags (and impersonating someone is certainly against their rules, see: https://support.twitter.com/articles/18311
As for the DM communications, the scammer also picked up a nice passel of emails which he or she knows work. And those have probably been sold to a spamming company which buys mailing lists. So welcome to being spammed if you DMed this account!
For larger corporations, this is one of the many problems they have with social media.