Theres actually a mixture of styles in those nails.....the rainblow swirls are hippy, they're done with a striping brush or small detail brush and tiny lines drawn in each of the colours. There is a YouTuber who has done them but I can't remember which one....I'll have a search and try to link back for you.
ETA - I found this one, it's not the one I was looking for but it will give you an idea:-
The more 'square' shaped patterns are more Aztec than hippy so you might have more success in searching for Aztec rather than hippy. Google will give you a few Aztec stamping plates for instance from places like BornPretty, etc.
The dot ones are ying & yang which is an Indian symbol for 'both sides' - light & dark, male & female, good & bad, etc. and again there are stamping plates available on a google search.
As you can see it's a mixed bag which is probably why you won't find one plate to do all 3 styles.