How to sync two animations using css keyframes?

Mathematically speaking, sinking means adjusting frequency and phase. I'll demonstrate each separately. Note that what I'm gonna explain is the concept and you can implement it in your codes using Javascript, css, etc

Frequency

You can't sink two animations unless the longer duration is a factor of shorter duration.

For example in your codes, blinking has a duration of 1s. So your image scaling duration and Also the whole duration must be a selection of either 1s, 2s, 3s, ... or 1/2s, 1/3s, ...
For better understanding let me make a simple example. Assume two images want to be animated.

<img src="1.png" id="img1">
<img src="1.png" style="margin-left: 50px;" id="img2">  

Consider two different animations for each one

@keyframes k1
{
    25%
    {
        transform: rotate(-4deg);
    }
    50%
    {
        transform: rotate(0deg);
    }
    75%
    {
        transform: rotate(3deg);
    }
    100%
    {
        transform: rotate(0deg);
    }
}

@keyframes k2
{
    50%
    {
        transform: scale(1.2);
    }
    100%
    {
        transform: scale(1);
    }
}

So since k2 is simpler, I'll first assign it to img2 with duration of 0.7s

#img2
{
    animation: k2 0.7s linear infinite;
}

And based on what was explained, I will assign animation k1 to img1 with a duration of 1.4s. (NOT 1.3s NOT 1.5s VERY IMPORTANT!)

#img1
{
    animation: k1 1.4s linear infinite;
}

If you run this code you'll see they are sink! To feel the concept better, change the duration of k1 to 0.9s. Now it feels like they are doing their thing separately!
Note
I set k1 to 1.4s (0.7s × 2) because k1 seems to be a combination of one go forward and come back and using 2x feels they are dancing together with the same harmony!

Phase

In css, phase is showed by animation-delay. Modifying frequencies (duration) is enough to sink two animations but if two animation begin at the same time it will feel better! So to illustrate set a delay for img1 of 0.2s. They are still sink but it doesn't feel nice! Now change the delay to 0.7s. Now it's beautiful again! (Maybe even more beautiful)

Back to your code

Your images scale with duration of 1.2s (40% of 3s) and your text blinking duration is 1s and as you can see they are not factor of each other so you can't sink!