It depends on the type of flag, and why it’s been flagged.
For Off Topic Posts, it doesn’t really affect anything at all, other than that post itself.
For Inappropriate Posts, it can lead to temporary or permanent restrictions for the ability to post on the Forum, and can also remove or block Regular status.
For Spam Posts it can lead to the inability to create new threads or a permanent ban, depending on the nature of the Spam, and can also remove or block Regular status as well.
In all cases, the maximum repercussion before a moderator or Staff reviews and approves the flag is a post being hidden. That happens automatically if the Forum software deems the flag(s) sufficiently trustworthy, which it judges based on the quantity of flags on the post, and the historical trustworthiness of the person or people who submitted the flag(s), based on whether their past flags were deemed accurate.