No... but sort of... That is to say, for a slave in the antebellum American South, it is less straight forward than you might think.
Strictly speaking a slave was bereft of honor, and honor was a prerequisite to duel. The duel was on the one hand an expression of freedom and bodily integrity, and the other hand a mechanism of enforcement for social norms and conflict resolution, and the dueling class quite explicitly defined themselves in opposition to the slave class. The duelist, in challenging another, was expressing several things: Firstly, his own standing as a gentleman and mastery of self, secondly the offense caused by his opponent but that his opponent was nevertheless essentially his equal, and third, his compliance with community expectations of behavior. He controlled his own life, and his own destiny, and was willing to stake his life to defend his word. The duel served both to express this freedom, and also to control men of the planter class through self-policing of their behavior. I'm fond of Bertram Wyatt-Brown's characterization of the slave society of the South:
Policing one's own ethical sphere was the natural complement of the patriarchal order. When Southerners spoke of liberty, they generally meant the birthright to self-determination of one's place in society, not the freedom to defy sacred conventions, challenge longheld assumptions, or propose another scheme of moral or political order. If someone, especially a slave, spoke or acted in a way that invaded that territory or challenged that right, the white man so confronted had the inalienable right to meet the lie and punish the opponent. Without such a concept of white liberty, slavery would have scarcely lasted a moment. There was little paradox or irony in this juxtaposition from the cultural perspective. Power, liberty, and honor were all based upon community sanction, law, and traditional hierarchy as described in the opening section.
But, while slaves couldn't properly duel, they would sometimes find themselves in pantomimes of the ritual. It was not unheard of for masters to arrange for what Kenneth Greenberg calls a "Not-Duel" - staged farces for their amusement. Two slaves - usually forced into drunkenness - would be forced into causing an "insult" and the other "challenging" over it. A fight - without weapons - would then be arranged while the white men watched and bet on the outcome. Serious injury, let alone death, was to be avoided and the fight would be broken up when it had gone far enough, often with a whack of the cane. In actuality, these fights are more akin to a boxing match (although with little rules - kicking, headbutting, and most other forms of fighting were allowable), but in dressing up the fights in the language of the duel, the masters made a show of power, the slaves not acting out of their own freedom, but at their master's whim. In Greenburg's words, these arranged fights "pleased gentlemen of honor to witness the emptiness of such an encounter-an emptiness that confirmed their own fullness."
However, while slaves couldn't duel in the proper sense, they were not ignorant of the language of honor. As I said at the beginning, the duel was about more than simply exchanging shots. It was about how a man defined himself, and the most important aspect of ones' self-image was to have ones' word respected. To be called "LIAR" was one of the worst insults, and one of the most assured means of ending up in a duel, because it was to assert that their external presentation of 'Self' was false. Whatever the actual lie might have been, however minor, to call a man out for it was to assault his entire person. This was the language of honor, and it is not uncommon to find in slave memoirs and recollections, the framing of their acts of resistance in terms explicitly coached in that language. While not a duel in the formal sense of the term, in using the terminology of honor, the slaves certainly felt that they were, in their own way, dueling their masters, and standing up for their bodily integrity.
Frederick Douglass, in his memoirs, describes his time working for for Edward Covey, a notoriously brutal slave driver leasing Douglass for the time. After failing in an assigned task, despite his best efforts, the 16 year old Douglass was stipped and beaten. Further failures were similarly met, even after Douglass reported to his master what he believed to be unwarranted punishments for failures beyond his control. Finally, Douglass stood up to Covey though to defend his "manhood":
It was a glorious resurrection, from the tomb of slavery to the heaven of freedom. My long-crushed spirit rose, cowardice departed, bold defiance took its place; and I now resolved that, however long I might remain a slave in form, the day had passed forever when I could be a slave in fact. I did not hesitate to let it be known of me, that the white man who expected to succeed in whipping, must also succeed in killing me.
According to Douglass' account, it worked. Douglass presented Covey with defiance, and Covey backed down, although to be sure, he was in part saved because of Covey's own brutality. In standing up to Covey and asserting that he must kill Douglass in order to succeed, Covey's reputation - his external presentation of self as a hard slave driver who could break any disobedient slave - was challenged. To kill Douglass would be to lose that image, and thus Douglass' act of resistance, his assertion of his own mastery of his life or death, placed Covey in an impossible position. While not a duel per se, it nevertheless was the utilization of the language and culture of honor that ruled masculine culture in Southern society. True dueling was cut off from slaves in the American South, and many "dueling" encounters were nothing more than puppetry by their masters, but nevertheless, the culture of honor was penetrable in some ways by those living in bondage, and at least some of them managed to utilize it in some ways.