No they would not be compatible. The black ghost knife is MUCH too aggressive and would kill the betta. The betta is considered to be a semi-aggressive fish most times with fish of their own species, but the black ghost knife fish is aggressive all the time. Knife fish are generally considered to be of the type of single species tank fish. (only the knife fish in the tank, perhaps more than one but only that species!)
A ghost knife needs a really really big tank and while it can hang out with some larger tougher species a betta is not one of them. Also once it gets bigger it will start swallowing whatever will fit into its mouth, which includes bettas.
I found 2 species of Black Knife fish in my books. The SMALLER of the two is listed as reaching 26 cm or a little over 10" in length. The other one will reach 47 cm or 18.5" in length. Now the Betta gets a length of 6 cm. or a bit over 2". That does not seem like a fair match, now does it?? The Black Ghost Knife Fish will make a meal off the Betta and you will be very sad (or you should be)... .
I know the idea seems cool--having a fish with long flowing fins with another fish that is knife shaped and can swim backwards, but basically bettas will be lunch for the ghost knife. They have large mouths proportionally as it is, it wouldn't even need to be fully grown to chow down on a betta.