"... one of its kind..." or "......a one of its kind."

Solution 1:

Hyphenated adjectives

Adjectives like "one of its kind" should be written with hyphens, to remove the exact problem that's making it difficult for you to make a decision here.

To make your decision simpler, replace "one of its kind" with "yellow", a one-word adjective, and look at your two options again.

• We are yellow app ...
• We are a yellow app ...

It obviously should be "a yellow app". Now that you've established that you need the article "a" in place, change the adjective back again.

• We are a one-of-its-kind app ...

We're an app?

Your sentence is grammatically correct (with "a"), but doesn't make much sense, even for advertising copy. "We", normally used to for a group of people, really cannot be "an app", a piece of computer software.

I'd suggest a different verb:

• We make a one-of-its-kind app
• We have created a ... the change in tense to past-perfect suggest you've achieved this just recently
• We offer a ...

Isn't everything "one of its kind"?

Finally, "one of its kind" is probably not the description you want. It is not an idiom in English, and so it has its literal meaning: just one of (possibly many) things of the same type.

The very similar "one of a kind" is the phrase that has the idiomatic meaning of "unique".