Instagram does allow you to use affiliate links in your bio and on your stories but there are some programs they have banned. So you’ll have to test whether they allow you to add the one you want, if the page gives an error, then this could be because of that link. So you’ll have to test it.
This video answers the question ‘are affiliate links allowed on Instagram?‘ and gives some tips on how best to use them:
Having more than 10,000 followers allows you to use links in your stories but don’t be tempted to buy cheap followers. Doing that could get your account banned. Always try and grow organically without any paid followers.
So, affiliate links are allowed on Instagram, just be mindful that there are some programs they don’t like.