Sup nice voice.
There are a few choices, for this particular song, false fold distortion is probably what would work best.
The thing is, one of the keys to controlling distortion well, is to have a good clean voice that can do the job on it´s own. So I would work first on getting more energy on your normal voice, going for a more yelled/shouted quality, and then looking to get distortion and other effects.
You can practice something simple, use vowel OH or EH on your middle range, it will get kind shouty. Then change to vowel AH trying to retain the same energy of the previous one, it makes it easier for distortion to appear. It should not hurt, if it does, stop, try again some other time.
You can also get the effect to appear by bringing the back of your tongue against the back of your throat, and elevating it, while releasing air as if you just had a very refreshing drink, something like "ahhhh". As you do it, a rasping sound should appear. It also should not hurt. Get the hang of it and then try to make voiced sounds with this on top.
Distortion is not different than articulating other rolled consonants, it´s just done very close to your vocal folds so if it´s not done well it can hurt. So as you practice it, be mindful of your limits and never overly rely on it.
I hope it helps!