@f29919fc 
IDK about a burn button, but firefox has an option to clear site data when closed, you can add exceptions to that. I imagine you can do something similar with Vivaldi.

You can also containerize different sessions with the "Firefox Multi-Account Containers" extension to create a container, do the stuff you want to do, then delete the container.
https://addons.mozilla.org/en-US/firefox/addon/multi-account-containers/?utm_source=addons.mozilla.org&utm_medium=referral&utm_content=featured
 
I know this isn't exactly what you want, but hope it helps 

 @1ac6a91f Unfortunately the setting of exceptions is way more cumbersome than what DDG supports (plus I don't know if that applies to ad blocking or also cookie clearing?). 

 @f29919fc 
It wont affect any ad blockers since that is presumably an extension, but it will clear cookies of any site not in exceptions. 

Also I realize its not really convenient, but I'm not sure of any other way to replicate the burn button. Though it may exist