Amazon quietly launched their own Influencer program (Beta) and I'm excited to know more about this. Though I'm not exactly a Social Media influencer, I would love to experiment with as many 'monetization' options as possible.
Right now they are displaying this message due to high submission volumes:
"Thank you for expressing interest in the Amazon Influencer Program! Due to the volume of submissions, you will only be contacted if you are invited to the program."
But still, you can just sign up for Amazon Influencer Program (Beta) and wait for their email, worth a try!
Before signing up, you can complete your current Amazon profile first, verify your email address, fill all your profile details, especially the "Social Media" field.