Electrical – connect two load lines to a GFCI receptacle

The first problem is that you may be using the wrong cable and breakers. NEC calls for 2 20Amp small appliance circuits in the kitchen, to accomplish this you'll need to switch to 20Amp breakers and #12 wire.

The next problem. You'll have to pull new wire anyway, if you want to hook up GFCI receptacles. GFCI receptacles will not work properly with a shared neutral, you'll end up with nuisance tripping with a shared neutral. GFCI receptacles work by monitoring the balance between hot and neutral, so if the neutral is shared the GFCI will not work properly.

To wire up the kitchen properly, you'll have to pull 2 new 12/2 cables from the breaker to the kitchen (all #14 wire on that circuit will have to be replaced). Then install 2 20Amp breakers, to supply the kitchen. You'll install the GFCI's as the first receptacle on each circuit, which will protect all downstream receptacles.

You can share a neutral between 2 GFCI receptacles. The catch is you'll have to pigtail the neutral to the receptacles, not use the neutral from the load side of the first GFCI to feed the second.

So you should be able to do something like this...

But not like this...

You'll then be able to use the load side of each receptacle to feed other devices, like this.

Let's see if we can answer this in pictures. For one feed from the breaker panel, to have each of the outlets on their own GFCI, you want this:

For one feed from the breaker panel to have one GFCI protecting downstream outlets, you want this:

However, you say that you have a red and a black wire in the box, and this complicates things. You might have a MWBC (multi-wire branch circuit) feeding the outlets, with the red hot on one outlet and the black hot on the other:

Or, you could have something else in this outlet, in which case (espcially if you don't feel confident) you really need to contact an electrician to get it sorted out.