As I wrote here, Kant writes in German, with Latin sentence structure (for example, the subject-reference of subsets of sentences is typical Latin style) but using German grammar within subsets of sentences. Thus, his style of writing is certainly strongly influenced by the Latin language used in almost all major philosophy of the time.
In fact, Kant is far from being the first to publish in German. Notably, Wolff started with German lectures and publications and only changed to Latin after there started to be wider, European attention to his ideas. As Conifold notes in a comment, the Latin versions never reached the same level of popularity though, so this experience might have contributed to Kant changing the language of his publications much earlier.
The main reason for writing in German at all is that since Pufendorf, there was a wider enlightenment movement which emphasised the equality, dignity, and education of the broader populace as a goal, a movement which was boosted even more by the Prussian state after Frederic II took over in 1740 (who, by the way, spoke mostly French at court as the French court was seen to be the most distinguished and he wrote and spoke in person with Voltaire, whom he admired much).
Since only few, usually expensive or theological schools taught Latin on an academic level, writing and teaching in German seemed to be a natural thing to do if you want to reach and educate a broader part of society.
Note that Germany was comparatively late in that: significant French, British, Italian, and Dutch philosophy was published in the native languages (sometimes much) earlier than that. For example, Kant had to wait for a translation of Hume being published in German before being able to experience his "awakening from the dogmatic slumber".