There isn't a single, universally accepted Gaelic spelling for "Kathleen." Gaelic encompasses several dialects, and the best translation would depend on which one you're aiming for. Furthermore, "Kathleen" is an anglicized version of names with Irish origins.
The closest equivalents would likely involve variations of Caitlín (pronounced roughly "Cat-leen") which is common in both Irish and Scottish Gaelic. However, the exact spelling and pronunciation might vary slightly depending on the dialect.