According to The Athletic Barnsley are one of several clubs considering legal action against the English Football League if they are relegated this season. However, the report states that Birmingham City, Derby County and Sheffield Wednesday will be allowed to start next season in the Championship on minus points because of financial fair play sanctions (the sale of stadiums to sponsors).
Derby are 12 points clear of Charlton in 22nd and Sheffield Wednesday are three points worst off than the Rams.
It is not clear on what basis the legal action could be brought (Hearts are also contemplating legal action given their relegation from the SPL). Just because something is unfair or rough justice does not mean it is illegal. Legal actions often succeed on procedural grounds, but I cannot detect any prima facie procedural failures.
With Charlton locked in a civil war and fast running out of money, the Addicks are in no position to launch a legal action about a points-per-game relegation. I am also doubtful whether any such action would succeed, although I am not a lawyer and just expressing a personal opinion.