Should I use the "a" article after "Some kind of"?

Generally no, but it is entirely governed by what comes next.

Some kind of loving

Some kind of magic

Some kind of a situation is developing, Houston.

I couldn't say. You didn't include the part that matters most.

The article depends on the noun that follows it. I can think of examples where an article is required, where it's forbidden, and where it's optional.

If you're asking whether "a/an" or "the" is appropriate after the phrase "some kind of", then yes, "a/an" is the right choice. However, if you're asking whether to use an article at all, the only good answer you'll get is: it depends.

If it's "Some kind of a ...joke"---yes. You use "a" before nouns beginning with a consonant. If the sentence is "Some kind of an...apple," you use "an," because "an" is used before nouns beginning with a vowel. "The" is specific, and used with every noun. "I like the joke" or "I like the apple."

Only if the next word starts with a constant and use 'an' if it stats with a vowel.