Did the angels say anything about reincarnation?
Not as such. However, they did say that clusters of personalities incarnate together primarily because the whole gift of one particular aspect of the Soul cannot be embodied by one being. Occasionally there is an ascended master who incarnates (Jesus, Siddhartha Gautama, The Prophet Mohammed) who incarnate alone, but most of us have little soul families with whom we incarnate. Whether we incarnate many times, or whether we retain the same personalities or histories after our lifetimes, the angels didn’t say.