Rename taxonomy name (slug?) due to spelling error

I am wondering if we are able to safely change the name of a misspelt taxonomy and avoid any broken links or SEO problems?

This page indicates you can do it BUT it says to flush permalinks which is BAD for SEO?

https://wpsites.net/wordpress-admin/change-custom-post-type-or-cpt-taxonomy-permalink-slug/

The page I need help with: [log in to see the link]