Thread or threads?

The singular form (ex. "thread") is generally preferred but the plural form (ex. "threads") is not wrong. Sometimes it depends on context.

When I worked in a fabric store, a customer might ask me, "What kind of thread do you stock?" In this case we would be thinking of thread as a unified category.

Now that I am working for an engineering company making cylindrical oil well components that screw together end to end, a customer could ask me, "What kind of threads do you stock?" In this case we would be thinking of the different types of screw threads that would be cut into the ends of the components.

In all cases it's considered more correct to use "type of" or "types of" instead of "kind of" or "kinds of."

'thread' in this case, is already plural, so I would stick with 'kinds of thread', rather than 'kinds of threads' (which really doesn't make sense when you read thread as plural and not singular'

Thread.

kinds of screw threads

There seems to be a little confusion here. The word "thread" is not plural. It is never plural in any context. The issue is one of countable vs. uncountable nouns. It's especially confusing because thread can be either a countable or an uncountable noun.

Countable examples:

"How many threads are you weaving together to make that rope?"

"How many threads per inch does that nice bedsheet have?"

Uncountable examples:

"How much thread is in that spool? Fifty yards?"

"How much thread do you have in stock?"
"Over ten thousand yards. We carry at least fifty spools of each color"

As to the original question, I imagine "threads" would technically be correct, but "thread" would probably be better since you are likely using thread as uncountable. Imagine buying different brands of bottled water at the supermarket and asking how many different kinds of water they carry. You wouldn't ask how many kinds of waters.

Oh, and in "...kinds of water...", water is singular. Kinds is plural. The same is true for "...kinds of thread..."