Ummmm in short no, nothing mixes well with a parrot....
Angels are finikey... they are also nippers, and although they are SA cichlids they act more like Africans with their little velcro like teeth and nippy pick your fins off behaviors....
Parrots are a cross bread of (you will get varied info on what is crossed into them, they are imported from Japan and no one will confirm) but Red Sevrums + ??. They are south American Cichlids, and behave like South American Cichlids. The caviat to this is that the cross breading that produced that cute little beak also made that beak unable to close properly. So your parrot has the mindset of a big mean guy, but no ability to bite back. They tend to resort to bashing things with their heads much like a flowerhorn. They really need to be kept in a species specific tank only for parrots.
They do have quite the personality, and like Oscars are interested in the world outside the tank. They can get pretty nasty, and they also spawn like CRAZY although they are sterile so they eggs will never hatch.
Angels are nippers, they have teeth like the old world cichlids and will peck your parrots fins to death. The parrot may or may not smash them into someting because it is annoyed.
Also expect in less then a year that that parrot will be the size of a large Man's hand... He would need 40G for himself... You may be able to squeeze 2 parrots into one 40g, but that would be it.
So in short don't buy the parrot unless you are making a parrot tank or your angels have died off...
