It is hard to say that the Duchess was flirtatious. Perhaps she was only friendly and in love with life. Either way, the Duke wanted her to only show affection to HIM. Take a look at the lines below and make your own judgment:
She had a heart--how shall I say?--too soon made glad, too easily impressed; she liked whate'er she looked on, and her lookes went everywhere. Sir, 'twas all one! My favor at her breast, the dropping of the daylight in the West, the bough of cherries some officious fool broke in the orchard for her, the white mule she rode with round the terrace--all and each would draw from her alike the approving speech, or blush, at least.
She seems very likely in love with nature, life, and small kindesses. What made him mad was the fact that she ranked his approval for her with everything else--sunsets, cherries that someone brought her, riding her mule. How dare she! (Smile)
What a wonderful poem! In the poem, the Duke of Ferrarra, a place in Italy, is speaking to an emissary (spokesperson). The emissary works for a man whose daughter is to be engaged to the Duke. The Duke is showing the emissary a portrait of his last wife. He talks about the qualities of the Duchess as they look at the picture. Appartently, the Duchess was flirtatious in nature. She has a blush upon her cheek that he believes is part evidence of her flirtation with the painter himself. He explains that everyone was equally likely to receive attention from her. He is obviously angered by this. He says that the Duchess showed a lack of respect for position - the Duke's name and nobility should have guaranteed that she show more attention to him than anyone else.
The Duke explains that he tried to stop her behavior, which demonstrates his need to control her; however, his attempts met deaf ears. So, he had to stop the behavior himself. We don't know how he did so, but there is a suggestion that he ordered her death.
As the poem wraps up, the Duke suggests they again discuss the upcoming marriage. It would seem that the Duke's explanation of the portrait could serve as a warning for the emissary to bring back to his lord and the new bride - behave, or face the consequences!