Can I play the campaigns in the normal hd mod through custom campaigns or do I need to use the original chronicles?

Heroes Chronicles is a stand-alone series from HoMM III. It can't be run through the HD Mod, but someone has developed a separate HD Mod for Chronicles, as I mentioned in this thread: https://www.speedrun.com/heroes_chronicles/thread/3dh85

I haven't looked into running the campaigns through the main game, but my opinion is the run wouldn't be valid. Unless the campaigns carry over the same bonuses/stats/characters as the original campaigns, instead use the Chronicles HD Mod.

If you can run and record Chronicles successfully, then by all means. For HoMM III, we allow the HD Mod due to ease-of-use and reliability to play/record due to how old the game is.