The influencer program is an extension of the associates program that you have to qualify for. Sam qualified with his youtube channel, he has 722k subscribers. You can probably imagine he makes a substantial income from amazon even at 4% commission
Currently you have to qualify with either YouTube, Twitter, Facebook, or Instagram. I am sure they will add pinterest at some time. From what I read they look at subscribers, followers and other metrics to determine if you qualify or not.
Once accepted you "Own" a page on amazon. So I guess it is time to become an influencer.
here is a link to the program if you want to read about it https://affiliate-program.amazon.com/influencers