If you have a green card in America and you want to sponsor your sibling and their children to join you how long does it take?

a person with a green card can't sponsor their sibling

It would take three to five years to naturalize (depending on how you got your green card) then once you were eligible to sponsor a foreign relative (because you have to be a citizen to do that) the processing time would vary depending on what country this sibling is coming from. But generally at least a decade. 

It would take at least a decade, and you can only do so once you're a citizen, not on a green card.

Only citizens can sponsor a sibling. After you become a citizen, you can petition for your sibling if you can prove you earn enough to support self + all dependents + your sibling, and have a suitable home for you all. Since it currently takes about 14-25 years for a sibling petition to become current, your sibling is not bringing any children. They will have aged out long before they ever get an interview for an immigration visa. Since any child will be an adult by then, your sibling will be leaving children behind until they get citizenship & can file a petition. Never-married adult child of a US citizen currently takes 7 years or more. Length of time for a Priority Date to become current depends on their citizenship. But by the time you get citizenship, then your sibling can immigrate (IF approved & receives a visa), then gets citizenship, then petitions for their adult child, it could take about 4 decades. 

It is not possible. Only citizens can sponsor siblings. It takes 15 to 25 years, depending on what country they are from. The lines are longer in some countries.