Trying to wire switch outlet combo to existing two outlet. But the outlets each have 3 wires
Let's take a look at what we have here

You have 2 cables, and each one has (presumably) hot, neutral and ground. It is normal for all grounds simply to be all tied to each other; 

The old device is definitely a GFCI or AFCI, no doubt of it.  

So what you're viewing as "each socket powered by a separate cable" is actually the GFCI device being what it is.  It has one hot/neutral pair (called "LINE") that inputs power from the supply, and from there, power goes through the GFCI electronics. The output of the GFCI electronics provides a zone of protection, and that goes to the other hot-neutral pair (called "LOAD") to be carried onward to other outlets.  It also protects the sockets on GFCI receptacles (not every GFCI device is a receptacle). 

So each cable does not power each socket at all. The positions are sheer coincidence. Both sockets are connected together along with the LOAD wires, and all together are on the protected side of the GFCI. 

Any socket-type outlet in the protected zone requires a "GFCI Protected" sticker. 

And this actually caused you to waste a lot of money.

GFCI Roundup

It sounds like you have way more GFCIs than you have circuits. That will cause you problems when a GFCI trips for cause ,because all the upstream GFCIs will also trip, and they are very picky about reset sequence.  

See this answer for how to untangle that. 

Now that you have a pile of GFCIs, identify every circuit in your house that doesn't have any GFCIs at all, and spread the love by finding the first receptacle in the chain. However do not put GFCI protection on safety devices such as refrigerators, radon pumps, fire alarms, etc. where a nuisance trip will poison or kill people. 

Grandfathering: you can't downgrade

ALL kitchen receptacles are required to be GFCI.  Even if this outlet was grandfathered, you can't downgrade: you can't remove protection you already do have. This means 2 things: 


This receptacle must remain GFCI
The downline circuit must be protected by GFCI


Now as the other answer describes, the other receps could be protected merely by siting a GFCI at the next recep. However, this recep still needs protection.

Fortunately, a dual GFCI+receptacle+switch is indeed an item that is sold.  It is exactly what you have there (the new one) but with GFCI protection on the receptacle.   The wiring to the screws is the same as the old GFCI receptacle.  The switch is not on any screws; it is handled as two pigtail wires which you can do with as you please. Noting that hardwired lighting does not need GFCI protection. 

That 20A-keyed socket+switch is an expensive beast, having just bought one myself. Take it back.  You may find the incremental cost to a GFCI version of that isn't much more than what you are returning.