Usually users tend to do like this because they have paying campaign. Report it to the campaign manager so the user will get removed and get nothing, which i think he is really in a campaign or just wearing it.
He's not in any campaign. The campaign signature he's wearing only accepts participants from senior member rank and above. The campaign also demands that each post be at least 150 characters; most of his posts are not even up to a hundred characters. He's been in the forum long enough to understand how it works. It's either he wants to get into a campaign and doesn't understand it, or he's simply a spammer.
As for forum rules, there's no rules for "burst-posting", unless the posts are considered and reported as spam. But if the posts are somewhat good, then there's no issue at all.
There's no way a person can make a reasonable post every 2-3 minutes. Anybody who creates multiple posts with a three-minute interval between them is a spammer, because you can you can read a post and a few comments and write your own post in under three minutes. The account should be reported as a spammer.