Hi Z2061,
Thank you for participating in the Apple Support Communities. We understand when you flag or delete an email on your iPhone, it's not syncing to your other devices. We recommend restarting all your devices and making sure they have the latest OS version. If that doesn't help, you may want to delete and re-add the mail account on your iPhone to see if the issue persists after doing so. This bottom of this article has the steps: If you can't receive email on your iPhone, iPad, or iPod touch - Apple Support.
"Remove your email account and set it up again
- On your computer, sign in to your email provider’s website. Make sure that all of your email is there or make sure that your email is saved somewhere other than your device.
- On your device, go to Settings > Mail, then tap Accounts.
- Tap the email account that you want to remove.
- Tap Delete Account.
- Add your account again.
If these steps don't work, contact your email service provider for more information."
Also, if you have a VPN app on your phone you may want to temporarily disable or uninstall it as this can sometimes cause syncing issues.
Take care.
