To make a cuckold story more engaging, you should focus on the details. Describe the small things like the expressions on the characters' faces, the tone of their voices. You can also introduce some unexpected twists. Maybe the cuckolded person discovers that there is more to the story than they initially thought. Another way is to build a complex relationship network. Include the relationships between the cuckolded person, the unfaithful partner, and their mutual friends or family. By showing how these relationships are affected by the cuckolding situation, you can draw the listener deeper into the story.
Add some mystery. For example, drop some hints early in the story about what might be going on but don't reveal everything right away. This will keep the listener interested.