"what kind of movie" or "what kind of movies"
what kind of "movie" or what kind of "movies" do you like?

That kind of "person" or that kind of "people".

I like a special kind of "serie" or I like a special kind of "series".

I'm confused which rule we have to use here, do we use plural or singular nouns in this case.

Question

"what kind of movie" or "what kind of movies"
what kind of "movie" or what kind of "movies" do you like?

That kind of "person" or that kind of "people".

I like a special kind of "serie" or I like a special kind of "series".

I'm confused which rule we have to use here, do we use plural or singular nouns in this case.

Answer

1) Which kind of movie or movies are both fine - but consider saying which TYPE of movie. 
2) That kind of person is correct, if you want to say people then say those types of people.  
3) Series is the singular and plural. I like a special kind of series or I like special kinds of series.

Answer

Here goes!
1)  You would say 'what kind of movies do you like?'.   If you were talking about other people (and more than one person) you would say 'what kind of movies do they like?'  If you were talking a bout a SPECIFIC movie, then you would ask 'did you like the movie?'

2) That kind of person, or those kind of people.  You can see the  difference here, when you are referring to a single person, or several people.

3)  'I like a special kind of series'   There is no word in English 'serie'.  Interestingly, there is an Italian word 'serie' as in the football league, 'Serie A'

I hope this helps, but just let me know if you need any more help. 
Geoff