Bugfender can work with any engine supporting the use of external libraries.
We've got little experience with Unreal Engine ourselves but their website offers information on how to use a static library on iOS:
https://wiki.unrealengine.com/Linking_Static_Libraries_Using_The_Build_System
On Android it seems a bit more involved: https://answers.unrealengine.com/questions/822567/ue420-aar-imports.html?sort=oldest