I am about to glue and nail down 3/4" plywood to my concrete slab as a sub-floor for 3/4" hardwood.
Pretty dumb question: Do i kerf the backs of the plywood boards in both directions (making squares) or do i just need to cut parallel to the grain/long ways? I'm going to kerf 3/8" deep every 12"

Who came up with that system? Ive never seen anyone kirf the back if you are glue and nailing it, I also dont see why you want to do that. There are more ways than one to skin a cat for sure so just asking. Have you tested the concrete? If you havent you better be careful, pulling up that type floor system is an absolute nightmare if it fails.

I talked to a flooring contractor who's a friend of the family and he suggested this. I was told there was really no other way to install hardwood on concrete as nails tend to loosen over time with the hydrostatic pressure in the slab so gluing is also a necessity. The only thing I'm worried about is lack of moisture barrier under the plywood with this setup (cannot roll out moisture barrier AND glue it down) but the family friend assures me it will be ok unless i get water under the slab. It doesn't seem to be an issue since the site is well graded and sits on a hill. During downpours the water tends to flow away from the house. I'm putting tar paper over the plywood and in the process of testing the concrete now, will have results in the next few days.
I though to kerf so that the plywood lies down flat, some is bowed in the middle. Kerfing was the one thing the contract had not suggested which i decided to add to the process. I'm assuming it's to help lay the plywood flat when gluing and to relive pressure so it does not want to pop up.

Why dont you hire the flooring contractor to do it then when it blows off the floor you have somone to blame besides yourself.

What other options exist for installing 3/4" hardwood on concrete?

Honestly I would first check the concrete for moisture then If needed I would roll a moisture barrier sealer on the concrete(probably do it anyway). The I would lay some 30lb felt over the concrete followed by two layers of 3/8" ply laid perpendicular to each other as a floated subfloor. then lay some aquabar B over the plywood and nail your floor to that. I dont like punching thousands of holes in the plywood and in the slab after Ive gone to all the trouble to seal it off. Before we learned how to float we would
mop on black mastic, layed 6mil plastic in the mastic, cut 3/4" ply into 2' x 8' strips then shot the ply down with hilti loads. It's an "old School" way of doing it but it's works. See them like this quite a bit in Florida.

My calcium chloride tests show:
2.6 lb/1000/24 hr
2.72 lb/1000/24 hr
and 3.08 lb/1000/24 hr

That is mostly below the threshold i have seen published that requires a moisture barrier. Is that right?

Yes, but remember, the values change during seasons, wet and dry. Plus did you follow directions on the placement of the tests? Lots of people simply plop the tests down.
For a truer picture of whats going on in the slab do a insitu test, like Wagner rapid rh sensors.