"Is maith liom a bláth" is "I like her flower". If I wanted to say "I like HIS flower" would it be "Is maith liom a bhláth"?
Yes, and Is maith liom a mbláth is "I like their flower".
For nouns that start with a letter that can't be eclipsed or can't lenited, you can't always distinguish.
I thought that might be the case but I've learned not to take every sentence I see here to be 100% correct.