The straightforward answer is:
All of your affiliate links are personal and you sign up (and get paid separately) to each of them (Amazon, AllPosters, Zazzle, Adsense, Chikita) except Viglink, which you sign up to through Wizzley (even if you already have an affiliate account with them) but get paid by Viglink.
I assume from your question that you have found where to place your affiliate links.
Wizzley earns their money by placing their affiliate account numbers in the links to those sites in a proportional manner. Your aff details are placed on the remainder of the links going to the sites. When you first start the proportions / ratio is 40:60, then 50:50, 55:45, 60:40 in your favour as the number of your articles increases.
Basically, just add your affiliate numbers in the places required; write some articles; sit back and hope they make money.