I though that the previous post was very strong. I think that such a question is open to a form of interpretation. I like to think that the emphasis brought out by the repetitition brings forth the idea of the angel delivering her own verdict on how human beings act on earth. Her repetition underscores the agent of the angel and it brings to light the idea that she, a messenger of divinity, is bringing some type of guidance and structure to the individuals on Earth who seek answers. Her use of the personalized pronoun configures where meaning and judgment ought to be. For example, Prior's absorption of self is interrupted when he hears her enter and is taken aback when he hears her speak and repeat the personal pronoun. In doing so, he begins to understand his own purpose and function, and move away from the focus of self into a larger element and design.
In the HBO adaptation of Angels in America and in the play itself, the angel always repeats this first-person pronoun. Your question is very good but also very specialized. You would probably do well to review several analyses by critics of the play or the televised series.
Sam Staggs, in his book When Blanche Met Brando, sees this repeated "I" as "a dazzling, otherworldly trope" as well as an allusion to the statement by Stella to Blanche ("I, I, I took the blows..") in A Streetcar Named Desire (327).
William W. Demastes, in his book Staging Consciousness, sees the repeated "I" both as contributing to making the angel difficult for us to understand and as reinforcing the content of her speeches: personal freedom can be destructive (126).
You can review these two sources on books.google.com. A better resource, of course, would be a good library that has access to the MLA bibliography and Academic Search Premier.
In any case, I'd be very interested in hearing how you ultimately make sense of this repeated phrase!