The search term ‘screaming frog affiliate program’ has 40 monthly searches globally according to KWFinder on Mangools.
It’s not much given the popularity of the software, but I thought I’d answer your question (and hopefully catch the featured snippet, too). So:
Does Screaming Frog SEO Spider have an affiliate program?
No. According to the FAQ on their website, Screaming Frog SEO Spider does not have an affiliate program at this time.
If you’re looking for affiliate opportunities with SEO tools, consider Mangools.