Where is there an example of dramatic irony and repetition in "My Last Duchess" by Robert Browning? Also what could be the theme of this poem?
Concerning Browning's "My Last Duchess," I'll cover theme in the poem for you and let another editor deal with dramatic irony and repetition.
The enotes Study Guide on the poem lists two prominent themes: Pride, and Art and Experience.
The speaker of the poem is conspicuously proud of his artwork. He begins and ends the poem showing works of art to his silent listener. The art is valuable even more for its reflection on the speaker, than for any artistic value. The duke wants to show off his good taste. He is excessively proud of his heritage, as well. He is so prideful he refuses to "stoop," as he calls it, and the price for making him even contemplate doing so is death.
The problem is also that the speaker thinks of people the same way he thinks of his art. This reveals the second theme: Art and experience. He is much happier now that his wife is reduced to a work of art, which of course, figuratively speaking, obeys absolutely. His wife would not behave like one of his works of art, so he destroys her.
Implied is the necessity for his new possession, his new bride-to-be, to grant the duke absolute authority and behave like a work of art.
The dominant irony in this famous poem is in the fact that the Duke is exceedingly proud of a portrait of his "last duchess" by a renowned (fictitious) artist named Fra Pandolf (a name he keeps repeating), and yet he had the beutiful young woman herself killed because he could not appreciate the real thing. I believe that all irony is connected with something that would be funny if it were not so painful and sad. Instead of appreciating the artistic merit of the portrait in our imagination, we, like the Duke's silent visitor, are horrified by the gradual realization that this innocent, lovely young human being, who loved life and deserved love and protection, was pitilessly murdered for no reason. Towards the end of the poem the visitor cannot restrain himself from jumping up and leaving the room without apology or explanation. The Duke follows him, still talking, and without understanding what a bad impression he has made. The Duke fancies himself an art lover, and yet he is a twisted, insensitive, remorseless egomaniac.