The translation in the link is correct at least for this sentence (I have not checked the other lines). This なれる is not (～に)慣れる ("to get used to ～") but the potential form of (～に)なる ("to become ～").
君のためなら 俺にでもなれる Billionaire
This line basically means the same thing as:
If it's for you, even I can be a billionaire.
You have to understand two grammar points here. First, "billionaire" has been pulled out for emphasis. This is an extremely common rhetoric device known as 体言止め.
Second, you can use に to mark the subject of a potential verb, provided the potential verb does not already have a に-marked term.
ビリオネアになれる ("can become a billionaire") already has に, so 俺にビリオネアになれる sounds unnatural (you usually have to say 俺はビリオネアになれる instead). However, its 体言止め version, 俺になれるビリオネア, sounds acceptable because there is no longer に after ビリオネア. Add でも after 俺に, and you get the original line.