People will have a difficult time responding to your question. As a literary figure in many Arthurian sources, Arthur's court was the epitome of Chivalry, and one would certainly think of him as chivalrous - although it would be best to refer to him as a chivalrous king rather than knight. The primary sources often focus on the shortcomings of those who aspired to the ideal of chivalry, but they also describe sincere attempts to remain honorable.

The problem with your question is that it seems to be structured as though you are interested in the "real" Arthur, whatever that means. Any real person (or persons) who helped inspire and establish the Arthurian cycle of tradition and literature was far removed from the ideal expressed in the literature. Such a person(s) existed long before chivalry was even a concept.

You may receive better response if you clarify the intent of your question - or perhaps my answer is what you're looking for.

Questions about the existence of King Arthur come up a lot. There was a recent discussion here, with u/Stormtemplar and some others providing some good input.