The closest thing to an account migration would be to create a kbin account and follow your previous mastodon follows. You should then be able to see their content in the Microblog tab.
The Magazines tab isn't present on Mastodon and there is no similar function there.
Not sure if related but I've see this exact issue with my personal lemmy instance. Federation seems to be fine but to and from kbin.social seems half-broken. I can open the magazine and some have a single post but most are empty.