With unequalized speed, Clark could just blitz, but with it equalized, I'm less sure on the direct result.
A lot of Supes' powers aren't exactly hax. Stuff like heat vision and ice breath are basic attacks and the ability to become intangible is something every daemon in 40k can do, so it's not like it's unfair.
The most dangerous thing to Supes here is Gorechild, since it seems to ignore physical durability (likely via similar properties to something such as Genestealer claws), be a daemon weapon at this point, and able to hurt enemies with the non-physical properties of daemons and such. I can't remember the exact degree of Superman's resistance to stuff like this, so I don't know exactly how hazardous this will be.
The most obvious thing Clark could do would be to press the extreme range advantage, though it's not in character for him to play keep away immediately with an unfamiliar opponent, so Kharn potentially exploiting that early portion of the fight could matter.
Is BFR allowed? Because that's quite possibly the easiest win option Superman has. Stranding Kharn somewhere in space and away from the fight won't kill him, but it would be difficult for him to reliably return under the normal timeframe, since he's not someone like Ahriman who can open and close Warp portals on a whim.
That aside, the BFR sounds like a fair point and from what I heard in other threads it's not OOC for Supes to do it. Sounds like a pretty even matchup but it's hard to know, could he do so before getting hit with the Gorechild or something?
Or would Supes resist it somehow?
EDIT: Guess my final vote depends on those resistance feats Matt said he would be bringing.
"I can't remember the exact degree of Superman's resistance to stuff like this, so I don't know exactly how hazardous this will be."
Superman has some insane feats of resisting Existence Erasure, that I know. I do know there's a feat where an embodiment of death is like "Now you die" to Superman and uses his powers to make people die instantly, and it doesn't work at all. Generally considered to be a really high-showing, tho.
Superman's will also made him maintain his own individuality within the Source, instead of becoming one with it.
By the way, Superman consistently is shown capable of surviving Darkseid's Omega Beams, which erase the target in body and soul. So Kharne would need to do some serious hacking and slashing to kill Supes.