How do I transfer photos from my iPhone 6 to my iPhone 13 withour iCloud?

No backups means your data has no value to you, or your data can be easily recovered or regenerated.

To transfer your content…

Load the photos onto a Mac or Windows system, then transfer them back to the new device.

Transfer photos and videos from your iPhone, iPad, or iPod touch - Apple Support

If iCloud Photos is not enabled, a backup should transfer the photos. The backup can be to iCloud, or to a local Mac or Windows system.

As should the quick start mechanism.

Transfer data from your previous iOS or iPadOS device to your new iPhone, iPad, or iPod touch - Apple Support

ps: Mailing photos tends to lose the resolution and/or require lots of mail storage, and it’s a lot of work for those of us that have hundreds or thousands of photos.

7-4-1776 Said:

"How do I transfer photos from my iPhone 6 to my iPhone 13 withour iCloud?: New phone. I do not have backup on iCloud. Need to get pics transferred."

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Some Thoughts:

eMail them to yourself. Or, use cloud service from a different source (i.e. your Internet Service Provider).