People get really excited about these cool twitter videos (for all characters, not just Chrom), and to be fair, there are a lot of great combos and setups in them. In reality, however, the vast majority of them are not true combos . I've been hesitant to report anything that doesn't register fully in training mode, which makes a lot of chars like Chrom and Wolf look like they don't have an amazing combo game.
But there is a reason these videos are being made. Those attack chains are connecting in real situations despite there being enough frames to dodge out or something. The reason for this is that defensive options are a lot worse this game, specially air dodge. So while some of the combos may not be "true", air-dodging during them would lead to dying offstage (huge recovery before you can upB) or landing but getting hit with something a lot more deadly.
The old smash 4 "bait airdodge" was one of the only few ways to get big hits in and that has been magnified a lot this game. The guessing game, mixups and relentless offense are going to be the main things to succeed.
So rest assured, even if Fair Fair Fair is not a true combo on Chrom, you have a pretty good chance of actually landing all 3 regardless, or even mixing it up with an F-smash or Ftilt at the end instead. It's gonna take more than just training mode to find all these amazing things out, so we're still just just scratching the surface of what many characters are really capable of!
So yeah, be hype for this character! But keep in mind his true strength lies elsewhere, in his great movement speed, good frame data and reliable hitboxes. The last one, specially, is what I think will make this guy be better on-stage than Roy, as he can get Uptilt and Fsmash to connect properly in A LOT more scenarios.