Bulk Download Pictures from Messages
I had this same issue and was able to resolve it by extracting the data from a backup. I used the script (accessible via link) to accomplish this. Note that a Mac would be required - Also note, I am in no way affiliated with the source or content, just a user in the past.


Run a phone backup via iTunes while connected to your computer
In Finder, go to the Go menu -> Go to Folder, enter in ~/Library/Application Support/MobileSync/Backup
Locate the most recently modified folder in the Backup folder
Create a folder named iOSBackup folder on the desktop
Copy the folder you found in Backup to iOSBackup
Download iOSMessageExport (zip) which includes a set of perl scripts. Unzip the files into the iOSBackup folder. (You should see similar to the screenshot below)

Open Terminal
Enter cd ~/Desktop/iOSBackup and press Return
Enter perl backup.pl --directory_path &lt;folder&gt;/ and press Return. Replace  with the name of the backup folder inside of iOSBackup (will vary from backup to backup)

Once the script has finished running, go back to the iOSBackup folder and look for a folder named _export

Inside of _export you should see folders for each date a message was sent/received, images/movies are located in here. HTML files of each conversation (by day) are also available



Source: WonderHowTo