I think theres no need to do the ICAO eng test again if you have done it earlier this year, the result should be recent enough to reflect your level of english 'today', you can inform KA about it, should you have passed your 1st interview, they will send you a cosent form to sign stating your agreement to let KA shares the result from CX. Thats what happened to me.
I guess I have just passed ICAO eng with CX(although no one had notified me about my result), plus having signed that cosent form, KA invited me to 2nd interview, done my medical check yesterday, and is looking for people who might be in the same batch for my group exercise on 17/11, so that we can gather and get prepared.
How long since you have done your aptitude test?