Null object

Well, that is a tutorial by an enthusiast that only partially explains how the sample video was created. It ignores the different speeds of the different layers so that the movement simulates the parallax shifts you would get with a camera moving across a scene. I'd give the tutorial and the explanation a D and an F for explaining how to replicate the demo videos. 

Your layer speed is controlled by how far the null moves over time. If you want the movement to speed up, you'll need to move the null farther along the timeline. You can do that by going to the last keyframe and adding more to the X value. If you want the movement to be twice as fast, then you need to double the X value. You can do that by just selecting the X value, using the arrow key to the last digit, and typing * 2.  

You need another null with a slightly different speed to get the parallax shift. 

I would use an expression for the layers that based movement on the layer's in-point and an even number of pixels per frame. No keyframes would be required, and moving the layer, a whole number of pixels per frame would prevent judder (jerky moves) and allow you to vary the speed based on the layer's simulated Z depth.

Something like this would move a layer from the right side of the screen until it completely crossed the comp panel. 

xStart = thisComp.width + width/2;
t = (time-inPoint)/thisComp.frameDuration;
ppf = 12;// pixels per frame
x = xStart - t * ppf;

[x, value[1]]

Changing the ppf value changes the speed. 

That is the way I would set up the movement.  I would also set up an if/else statement for opacity so that opacity would change to zero when the layer moves off the right side of the screen. I would also compensate for the scale in both expressions. 

If you want all layers to move at the same speed, I would just multiply the X value of the last keyframe by the speed increase you want. That is probably the easiest solution.

There are hundreds, if not thousands, of ways to create a slideshow. Without workflow details or a screenshot showing your timeline's workings, it is pretty hard to figure out how you are animating images using a null. Select your layers, press "u" to reveal the keyframes, take a screenshot, and copy and paste it to the reply field so we can see what you are doing. If you use a template or follow a tutorial, give us a link. 

We need more info if changing the distance between keyframes does not fix your problem.

Speed is distance travelled in a given time, so to make things faster you need to make the time shorter or increase the distance, i.e. put your keyframes closer together or use a huge value on the second key. Anyway, I suggest you really watch some tutorials.

Mylenium

I'm not sure what you mean. What exactly are you asking? Sounds to me like you need to study the basics on keyframing and create more of them instead just lettting everything move at constant speed with just two keys at the start and and, if that's what you're alluding to.

Mylenium