Amazon has a great program, that allow influencer to create a storefront page and getting pay with referal. This would be much more convenient for us to have Influencer to select the product and link directly their page VS doing doing referal product per product.
Does someone know a similar app or a company who have done something close and we could hire to customize ?
I don't know of an app / platform that does this but I like Refersion for ecommerce affiliate programs. It allows you to use links + coupon codes (great for Instagram influencers).
As for the influencer's own page, 1 idea is to host on your site, let them choose the products they want to create, get a description and profile photo and build them a collection. So it would be like a customized collection page they send traffic to.
Professional influencers will usually already have their own platform, whether blog or social media, so just affiliate link or coupon codes would be good.