Nobody knows, but that won't keep me from making a wild guess!
The obvious first thing to try is short fluorophosphine chains, like $P_3F_5$.You could turn that into a $-P_3F_4$ group ($R-PF-PF-PF_2$) attached to an appropriate carrier molecule. That's stable enough to not immediately dissociate like polyfluoronitrogens, and maybe you could get energy out of it by reacting with $HF$? To produce $R-PF-PFH + PF_3$, or $R-PF-PF_2 + F_2HP$. You'd get better solubility and more consistent chemical behavior by allowing a hydrogen substitution, so you end up with $R-PF-PF-PFH + HF \Leftrightarrow R-PF-PFH + F_2HP$.
I am disinclined to bother trying to figure out the energetics of such a reaction, though, because it has some significant problems; phosphate is just a generally useful ion to have around. It's charged, and participates in a bunch of catalytic reactions and it can form multiple bonds to build bridges between other molecular groups--like nucleic acid backbones. Phosphines are polar but uncharged, and don't have the same kind of functional diversity. It all comes down to fluorine just not being a good substitute for oxygen. However, if there is oxygen around (which there should be, because it's more abundant than fluorine and fluorine will displace it from water and silicates), then fluorophosphines will react with oxygen to form difluorphosphates ($F_2PO_2^-$), which is hydrolytically unstable in water (it wants to form regular phosphates and more hydrofluoric acid), but it is stable in hydrofluoric acid. These could probably be chained to produce something much more similar to terrestrial phosphate chains. Rather than
$R-O-PO(OH)-O-PO(OH)_2 + H_2PO_3 \Leftrightarrow R-O-PO(OH)-O-PO(OH)-O-PO(OH)_2 + H_2O$
$R-O-POF-O-POF_2 + F_2PO(OH) \Leftrightarrow R-O-POF-O-POF-O-POF_2 + HF$
In which we replace, not the oxygens, but specifically the hydroxyl groups with fluorines. Synthesis occurs by removing a fluorine from the chain and a hydrogen from the fluorphosphoric acid, using them to form new HF, and forming a new ester bond between the oxygen from which the hydrogen was removed and the phosphorus from which the fluorine was removed. Hydrolysis is the reverse.
I have no idea how to look up the actual energetics of such a molecule--I would be surprised if anyone has ever actually synthesized and studied it--but on general principle it should be slightly more rigid and have comparable if not slightly higher bond energy than Earthling phosphate chains.
And just to throw it out there, since I'm looking at it now, maybe you could do something useful with the nitrogen difluoride radical ('cause unlike polyfluorophosphines, polyfluoronitrogens like to dissociate).