Did he have some illness?
He has Spasmodic dysphonia
The muscles controlling his voice spasm. Diane Rehm from NPR has it too.
My first wife has it. It came on later in life. She couldn’t trace it back to any specific illness, injury or other cause.
My grandmother had blepharospam, which is related. Her brother and niece both had muscular dystonia.
In the 80’s she used to go to Duke Univ. medical every few months to get experimental treatments, which were injections of… botox, yes.
His sister Kerry also has it.
He reports having had spasmodic dysphonia for nearly 30 years, but only recently suggested it was due to flu vaccination - because everything bad medically must be due to vaccines.
Like the rest of his antivax crapola, the evidence doesn’t back up his claims.
Not to mention the millions of people who get a flu shot year after year and don’t have that problem. 
Not the heroin? Color me surprised.
My WAG about his voice is that so many people have throat-punched him over the years that his voicebox is permanently damaged.
Not that I advocate violence, but I feel RFK Jr. not having a voice (in both senses) would be a net positive for the world.
I imagine it helped.