I never knew that “skip counting” was a thing to be taught. I don't remember formally learning to “skip count.” I know I learned because I would see people do it when trying to count items. Like if I went to the supermarket with my grandma, she would count eggs by two when buying them.
I learned just because I thought it was cool, like a different way of counting. Then it just became practical to do it to count items faster. Skip counting aloud is good just to know the numbers, but it's also practical to count by 2s or 5s when you can easily identify a pattern, like the egg example.
If you want to encourage your little ones to skip count, then you should do it out loud every chance you get. Counting shoes, clothes, books, houses during a bike ride, etc. It's foundational to multiplication tables.
As we're doing homeschooling, I'm going over skip counting with the kids. Claire is a little familiar with it from her 1st grade in public school, but Oliver is still learning it. The homeschooling curriculum I'm following has a full lesson set to learn skip counting each week, it's part of their Algebra for Kids lesson.
We're on week 3 of learning skip counting, and the lesson has this video in it which I thought was really good. Most good teachers I've spoken to about homeschooling say that learning with songs is one of the most effective methods so I'm glad this curriculum uses them.
This is skip counting by 3, part of the Silly School Songs.
You'd probably ask why would I buy a curriculum when I can find videos online for free. The curriculum has a lot more guidance than just a video, but I wanted to give you this as an example. And I wanted to add it to my homeschooling links page as well.