flatpak calibre: Cannot read from /home/nicholas/in.epub (permissions?)
You are using wrong paths in command line.
The ~/in.epub and ~/ebooks/in.epub are different paths.
So you have to use correct paths:
flatpak --command="sh" run com.calibre_ebook.calibre -c "ebook-convert ~/ebooks/in.epub ~/ebooks/out.mobi"
or
cd ~/ebooks
flatpak --command="sh" run com.calibre_ebook.calibre -c "ebook-convert in.epub out.mobi"