Can I add citric acid to KCl for iron removal in a water softener?
Your ion-exchange column removes $\ce{Fe^{3+}}$ ions from your water by exchanging them for $\ce{Na^+}$. 

When you back-flush you use concentrated solutions of $\ce{Na^+}$ ions and citric acid to remove the iron out of your ion-exchange column. The flush water is waste of course which must be disposed. 

The exact chemistry mechanism of all of this depends on a number of factors:


NaCl has a solubility of 36 g/L at 20 C which is 0.62 molar but
KCl has a solubility of 34.2 g/L at 20 C which is 0.46 molar. 
I'd expect potassium citrate to be less soluble than sodium citrate but
I didn't find any data to support this notion in a quick search. 
I'd expect that you column has a better attraction to $\ce{Na^+}$ ions 
than to $\ce{K^+}$ ions.
If you have some sort of automatic monitor then it may not
function properly with $\ce{K^+}$ ions. I'd guess that the monitor
just looks to determine if the water is yellow, so I'd guess that 
$\ce{K^+}$ ions would work fine in this regard.
Not sure what pH you'd want. I'd guess maybe half trialkali citrate with
half dialkali hydrogen citrate to keep the back-flush solution
slightly acidic. 


All in all my guess would be that potassium/potassium citrate flush solution would work. I'd expect the column to need flushing more often. Maybe doing a flush once in a while with the sodium/citric acid mixture would give the ion-exchange column a good cleaning.   

The other consideration here is cost. Since the sodium/citric acid mixture is the common back-flushing salt, I'd expect a potassium/citric mixture to be more expensive.