Since moving my domain to cloudflare our G Suite custom domain emails continue to work, but when we send attachments the link to the attachment is broken and it takes us to a verizon search page with suggestions (verzon is just intercepting a bad link)
Cloudflare neither handles emails nor the web traffic to Google’s email platform, hence the issue won’t be Cloudflare related. I am afraid you need to discuss this with Google or the recipients of your emails.
This is, of course, assuming you are talking about email attachments. If you mean you embed in your emails links to your site, that might be a different case, but that would a) not be attachements and b) probably not a Cloudflare issue either.
Can you post a screenshot of such an email along with that attachment link?