What was the meaning of "I,I,I,I..." used by the Angel(s) in the HBO series Angels in America?

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.

For example:

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!