When playing the False Emperor flashpoint (in any difficulty, even Story!) you can unlock a secret bonus cutscene when entering the HK-47 Boss Arena.
To view the cutscene, you or a member of your Group must be using the Original/Vanilla Game HK-51 as their active companion when beginning the HK-47 Cutscene and you will get to view several extra dialogue cutscenes of HK-47 and HK-51 arguing with each other over who is the better Assassin Droid!
Using the after-KOTFE HK-51 Companion will not work as it is considered a different companion from your original class.

It doesn’t matter what faction or class you are playing as or even if you are using a different companion for the Flashpoint or the HK-47 Boss Fight after the cutscene, the only requirement is that someone be using HK-51 when beginning the cutscene!
You can view a video of the secret cutscene below from xLetalis on youtube: