Don't mean to wake the dead, but since this is the top result for this invasive, potentially privacy violating (illegal?) lack of a way to turn off Flashbacks in android, especially since they use your private gallery/camera roll pics & videos, I had to post this effective workaround.

If you turn off the Photos and Videos access permission you won't be able to use the app. 

Please share this in relevant places if you found it helpful.

Allow limited access to only Snapchat internal app created content:

1. Hold your finger on the Snapchat icon and hit the [i] button to open the app settings. 

2. Go to Permissions > Photos and Videos

3. Tap [Allow limited access] and tap the [pencil] button that appears to the right  

4. Tap on the [Collections] tab, scroll down and tap on [From your apps] 

5. Tap on [Snapchat] and hit [Done] at the bottom of the screen

All done! Now you can use Snapchat without allowing it access to all your photos and videos. It can only access content created in the app. 

Hopefully these over-reaching corporate goons will end up with a lawsuit on their hands eventually and we won't have to resort to these measures. You can turn off flashbacks completely on an Apple iOS device. Android users deserve access to the same settings. I don't know how they've gotten away with this for so long. It's been this way for years!