How do I automatically store photos from emails or texts directly to the Camera roll?
On iPhone, there's no way currently that I know of to automatically save images from Messages to your Camera Roll. However, you can save images in bulk from Messages to your Camera Roll:


Open Messages and select the conversation with the images
Select Details in the upper right (iOS 11) orTap on the top bar and then select the info icon that appears (iOS 12)
Lightly press and hold on one of the images you'd like to save.
Select More in the popup menu
Select the rest of the images you'd like to save
Select Save Images in the bottom left corner.