There is a rule against it, and apparently the league looked into it and concluded no violations, per Windhorst at least:The only way this makes sense (other than doing his buddy Rich Paul a solid) is if LeBron himself gets a cut of the contracts negotiated through Klutch, but I assume there's some rule against that.
https://www.cbssports.com/nba/news/report-nba-investigated-lebron-james-to-see-if-he-had-stake-in-klutch-sports-agency/