I use slightly different symbols than you,
but you can figure them out:
 
 1. K->L	
 2. ~KvF	
 3. (L&F)->A	
 4. ~A
      // ~K

 5. ~A->~(L&F)        3, contrapositive
 6. ~(L&F)            5,4 hypothetical syllogism
 7. ~Lv~F             6, deMorgan's
 8. ~L->~K            1, contrapositive
 9. K->F              2, writing a disjunction as a conditional
10. ~F->~K            9, contrapositive
11. ~Kv~K             8,10,7, constructive delimma   
12. ~K                11, idempotent law

Edwin