There's plenty of in-game precedence for keeping one ability while the other changes. However, there is also plenty of precedence for changing all abilities:
Lillipup: Vital Spirit/Pickup (Run Away) > Herdier/Stoutland: Intimidate/Sand Rush (Scrappy)
Elekid/Electabuzz: Static > Electivire: Motor Drive
Bagon/Shelgon: Rock Head > Salamence: Intimidate
Numel: Oblivious/Simple > Camerupt: Magma Armor/Solid Rock
I could go on...
Anyways, because all of the above have precedent, I feel it is safe to base this completely on flavour.
Reasoning for Embirch to have two different abilities from its evos outweighs reasoning for it to keep one or both. Embirch, unlike its evolutions, does not make sense to me having either Battle Armor or Rock Head. Obviously, it doesn't have very much armor, so that goes out the window. There's also the debate regarding Rock Head --- the only Pokémon to have Rock Head without having some sort of head casing is Basculin --- a 4th gen
So far the following have been suggested: Leaf Guard, Inner Focus, Weak Armor, Chlorophyll, Limber, Reckless.
Chlorophyll, as our TL pointed out, is for whole evolution lines
, with the sole exception of Cherubi/Cherrim, a rather special case considering Cherrim actually changes formes. Weak Armor is a 5th gen ability, so I don't think we're supposed to use that either.
This leaves Leaf Guard, Inner Focus, Limber
I'm more interested in the latter three, but I think any of those will work great on our little forest fire 'mon.