How do I stop my iPhone from saving pictures I send on iMessage

This is a setting within Messages that can be toggled on or off!

1. Please open Settings on your iPhone
2. Scroll down and tap on Messages
3. Scroll down and tap "Shared with You"

Shared with You allows content shared in Messages to automatically appear in selected apps. Once you open "Shared with You" you can select which content is shared to these Apple apps or you can turn it off for every app!

I hope this helps and answers your question!

Stop it from saving them where?