That prompt should include a little "Always" button at the bottom. Make sure Camera is highlighted and then tick that (or the other way around - I don't recall for sure). That will make sure that your stock camera app is always treated as the default.
If you get stuck jumping straight into Snapchat without the prompt, you can go to Settings > Apps & notifications > See all apps > Snapchat > Advanced > Open by default > Clear defaults to reset it.