Phrase Usage – Is ‘On the Same Level’ Natural for Skill Comparison?

Is it natural to use the phrase "on the same level" in sense of being as good at doing something as someone else?

Yes, the phrase is idiomatic, as Ronald Sole stated in the comments. And both versions are commonly used. Since the late 1960's, "at the same level" has been more popular in books than the other version (see the Ngram that Ronald Sole linked in the comments). "Level" means "someone's ability compared to other people" (Cambridge).

Note that the phrases are not only used to compare qualities between two people/things but also to compare the same person/thing over time.

I could keep playing at the same level until 50 years of age. - Zlatan Ibrahimovic

Could Love really play at the same level as Mahomes ...? - NFL Mocks

The corporate debt ratio in advanced economies has steadily increased since 2010, and now sits at the same level as the previous peak in 2008. - CNBC [The meaning of "level" here is slightly different, but it shows the comparison over time.]

Before moving on, it’s worth noting that Ben Simmons has the ability to play on the same level as LeBron James on any given night. - Philadelphia 76ers

Simmons will not be on the same level of rim protection Green ever was, but as a perimeter defender Simmons might have the upper hand. - Philadelphia 76ers

There are other ways you can write this. In your case, you can say

Kate and Tom are equally good at math.

or

Kate is as good as Tom at math.

You can also use the idiom "on (a) par with", which means "at the same level or standard as (someone or something else)" (Merriam-Webster).