I don't think there is a way for you to do this. When you delete a picture from a conversation, or even the whole conversation itself, it removes that information from your device. However, Facebook keeps this data stored on their end because whoever you are having the conversation with may still have that conversation active.
So if you and I had a Facebook chat going, and you sent me a picture, you could delete it from your end but it would still exist on my end. When you delete the app and then download it again on your device, Facebook brings that conversation back the same way Facebook is storing the conversation. So since Facebook is storing that picture as part of the conversation, when you bring your account back in the new app, it also brings those pictures back with the entirety of the message. Perhaps if you log into Facebook on a computer, you can delete the picture from the conversation there, and maybe it will keep it deleted on your iPhone as well. May want to consider contacting some sort of Facebook support.
That being said, if these pictures are part of your Photo Stream (iCloud), you can go to www.icloud.com and remove pictures there. This should also remove them from your other devices. But if you are trying to remove pictures from a particular app, you should contact the manufacturer of said app.
Best of luck
Delete photos from My Photo Stream - Apple Support
iCloud: Delete photos from My Photo Stream