The history of kink in Western poetry is a long and illustrious one, dating back through the Old Occitan (Provençal) troubadours of the eleventh and twelfth centuries. These pre-modern singer-songwriters frequently imagined themselves as serving / rendering service to / servicing noble ladies as though those ladies had the political power of the noble lords who were their husbands. In other words, the imagined (and probably wholly imaginary) relationship was one of dominance and submission between a Mistress and her serving man.
By the late thirteenth century, this paradigm had spread throughout Western Europe. It was so pervasive that misogynist (male) writers such as Jean de Meun attempted to straighten things out by putting women back in their place. Christine de Pizan, arguably the first feminist writer of pre-modern France, was of two minds. On the one hand, she approved of empowered women; on the other, she knew that that kind of power most often did not extend beyond the privacy of the bedroom into the public sphere. One of Christine’s successors, Alain Chartier, wrote a narrative poem, La Belle Dame sans Merci (or “BDSM” for short) whose thrust (so to speak) is that ladies should always grant their favors to lovers who beg sincerely.
If all this sounds a bit too ethereal for your taste, fear not—there is a whole genre, the fabliau, that is noted for scatological humor. Or, if you are into gore and torture, there are plenty of martyrologies to go around. (Warning: these scenarios tend to be non-consensual within the context of the fiction or the allegory. Or rather, if and when the martyr gives consent, they are consenting to the will of God, not necessarily to that of their human torturers.)
Flash forward to the nineteenth century, and we have Baudelaire, Rimbaud, and Verlaine—in other words, the usual suspects. Their twentieth-century emulators include Renée Vivien, Judith Teixeira, Alfonsina Storni, Gilka Machado, and Marie-Madeleine. I haven’t checked specifically for this, but I think it’s very likely that Emily Dickinson, Edna St.-Vincent Millay, and H. D. will also have some kinky poems, especially D/s, in their collected works.
Who is writing kink in today’s poetry scene? I’d recommend Patrizia Valduga, Poesie erotiche (Einaudi, 2018), in translation by Geoffrey Brock. I don’t know of any other poet with her panache, except perhaps Carol Ann Duffy in “Warming Her Pearls.”
Lyric poetry tends to be characterized by ambivalence, e.g. the blending of pleasure with pain. See, for example, Sappho’s Fragment 31. I wonder if all erotic lyric poems are always already kinky …