Your a bit shy on details, but trying to read between the lines, it seems that:
Both the old and new phones are non-smart phones, so there was no automatic backup to the cloud.
There was no memory card like an SD card, that might have stored photos.
You don't have a functional home computer to plug the phone into.
((((((((I didnt have battery power left to tell more--but your correct in all the above--plus my keyboard is sticking too. Neither phone has internet capability.)))))))))))))
If these assumptions are correct, there are two things you can do that come to mind, if you can still power the old phone and see the pictures on it.
If both phones have internal slots to add an SD memory card, you could copy the photos from the old phone to the card and move it to the new phone.
((((((((IM not sure what you mean being in not technically involved but will visit the corporate office on my next full day off--and see)))))))
Or, both phones almost certainly have Bluetooth, and the ability to send and receive the pictures wirelessly via a file transfer.
((((((((((((I THINK my ZTE does have blue tooth,not sure about the fliptop? I will give that a try)))))))
Good luck
Edit: In case you've never done Bluetooth file transfer before, it's usually easy, even on old non-smart phones.
On the settings menu of both phones, turn Bluetooth on.
On the old phone's Bluetooth menu, look for or tell it to scan for available devices.
Select your new phone from the list an tell it to pair with it.
Some form of confirmation will appear on the screens. Just follow the prompts.
Once your successfully paired, an option should be available on the photo to send the file via Bluetooth.
