Hi! This is my first post here, so if it's in the wrong spot, let me know. I also did a search and didn't find anything that would help me with this.

I'm about to be playing a Barbarian Totem Warrior and, for flavor reasons, I wanted the progression to go from totem attunement to Storm Herald. I'm happy to explain that in more detail if requested, but the basics are nature and animal spirit worship of his tribe. I know there aren't any prestige classes anymore and you can't multiclass into a different subclass. I was thinking that multi-classing into druid or ranger because of the nature connection or Bard because his rage manifests as singing songs of valor and glory while hitting things. I'm really not looking to add any kind of spellcaster as flinging spells just isn't his thing and I like the abilities that come with Storm Herald.

So, finally the question, any suggestions for copying the Storm Herald subclass into another class that would match with this character?

You would need to decide what subclass features from Totem Warrior you're going to keep and what features from Storm Herald you're going to keep. 

Totem Warrior has: (3) Totem Spirit , (6) Aspect of the Beast, (10) Spirit Walker, and (14)Totemic Attunement.

Storm Herald has: (3) Storm Aura, (6) Storm Soul, (10) Shielding Storm, and (14) Raging Storm.

If you wanted to swap Aspect of the Beast and Spirit Walker for Storm Soul and Shielding Storm, go ahead. Just keep in mind that some subclass features build off of previous features so you will have to account for that when recreating the features.

You’re not wrong, but I’m greedy and want it all lol

Oh, then that's a DM question not a homebrew question.

Ultimately it will be. I’m just trying to find the appropriate class to copy storm herald to. 

Why not just be a Storm Herald?

I’m already a totem warrior and can’t multi class to another subclass. Honestly, it’s not a super necessary thing and has a flavor reasoning behind it, but I just think it’s cool. The idea is that he’s starting off with a totem spirit and as that progresses becomes more attuned to the nature around him. 

Considering the level 6 totem warrior feature is kinda meh, I can see swapping it for a thunder bear build. Gives me the Thor vibes. 

Oh I just thought of an awesome hammer homebrew. 

Use an action to give yourself a flying speed that matches your movement speed till the start of your next turn. Use your bonus action to maintain that flying speed. Taking the attack action or any action that prevents your hammer from keeping you in the air will end your flying speed.

Or make it like a charge, super speed to any opponent within 30 ft. Kinda like flying at a dude and knocking the hell out of them with your weapon.