Hi Justin
The how-to of Patrick is correct - but as you are generating your sitemap using Screaming Frog there is really no need to go through this manual processing.
If you only need to create the sitemap:
Go to Configuration > Spider -
Tab: Basic settings: uncheck everything apart from "Crawl Canonicals" (unchecking Images/CSS/JS/External links is not strictly necessary but speeds up the crawl)
Advanced: Check "Always Follow redirects" / "Respect Noindex" / "Respect Canonical"
After the crawl - generate the sitemap - it will now only contain the "final" url's - after the redirects.
Hope this helps,
Dirk
PS Try to avoid internal links which are redirected - better to replace these links by links to the final destination
