Hi phishjams,
Thank you for contacting Apple Support Communities. Based on what you stated, it seems like iCloud emails are not syncing to the iPhone.
- Make sure that you're connected to the Internet. Try to open apple.com in Safari on your iPhone, iPad, or iPod touch.
- Go to iCloud.com on a Mac or PC to see if you can receive email for your iCloud email.
- Tap Settings > [your name] > iCloud and turn on Mail on your iPhone, iPad, or iPod touch. If you're using iOS 10.2 or earlier, go to Settings > iCloud.
- Make sure that new data is pushed to your device automatically. Tap Settings > Passwords & Accounts > Fetch New Data, and turn on Push. Then send an email to your account to see if Push is working.
- On your device with iOS 10, tap Settings > Mail > Accounts > Fetch New Data, and turn on Push.
- On your device with iOS 9 and earlier, tap Settings > Mail, Contacts, and Calendars > Fetch New Data, and turn on Push.
- Go back to Fetch New Data. Then Tap your iCloud account and turn on Push. If you have multiple iCloud Mail accounts, you can use Push with one account at a time. Make sure that Push is turned on for your primary iCloud Mail account.
- Turn your device off and back on.
If you still can't send or receive mail, turn off each of the settings in steps 3, 4, and 5 above, then turn them back on. "
Get help using iCloud Mail
Please don't hesitate to let us know if the steps resolved your issue or if you need additional assistance.
Cheers.