There is a simple reason why there are no documentaries about it, its often the same as for adults.
It is called "Conversion Therapy"
It's simply an form of abuse compared to the sexual abuse of children by their parents, the inflicted traumas can be compared.
Some of those self proclaimed "institutions" even use tasers on sensible spots and/or "medicine" that inflict nausea on the "patients" while they are being confronted with homosexual material/ideas, the idea behind this is to "link" this kind of discomfort/pain with sexuality / homosexuality.
Of course there are also less intrusive ways but the idea to link discomfort/blame with homosexuality remains as the "key".
This therapy can cause the same mental trauma like those that are found on molesting victims. ( encapsulation, fear/shame of sexuality itself, inner hate against the people who are responsible and so on). Personally i consider it as "mental rape" with the difference that it takes longer, costs money, has a more fancy name and is legal.
So back to the question
"What are Christian homosexual re-education camps for children like?"
Quick Answer: they are like the end of the childhood and the start of some serious psychological problems buried deep within.