Is this use of present participle grammatically correct?

This participial construction is 100% correct and natural. The participle is used as an attribute to the subject of the main clause, "we" (or "a Zhongguancun-based English training school", but that doesn't matter because it results in the same meaning). It gives extra information about "we", just as an adjective would. This attribute is placed after its "head" (the noun or pronoun it modifies) because it is a sort of apposition.

A participial phrase function as adjective.

In the sentence you wrote, "looking for native English speakers from the US and Canada" has a similar function of "lying on the kitchen floor" in "she was annoyed by the crumpled newspapers lying on the kitchen floor."

In your sentence, "looking for native English speakers from the US and Canada" is referring to the subject of the sentence, we.

Using a participial phrase is a matter of style; you could write the sentence differently. (I am reporting different ways to write the sentence, without giving any suggestions about which one is better; the sentence using the participial phrase is correct.)

We are a Zhongguancun-based English training school, and we are looking for native English speakers from the US and Canada.
We are a Zhongguancun-based English training school interested in native English speakers from the US and Canada.
We are a Zhongguancun-based English training school; we are looking for native English speakers from the US and Canada.