Is Kuuk Thayyorre read from left to right?

You are likely asking about the writing system used for the Kuku Yalanji language, which is sometimes referred to as "Kuuk Thayyorre" (although the latter is more specifically a dialect within the language).

The answer is yes, Kuku Yalanji is written from left to right.

It uses the Latin alphabet, which is the standard direction for most European languages.