The first reference I have to Ayanna meaning "beautiful flower" is in _The Book of African Names_ by Chief Osuntoki, copyright 1977. In this book, Ayanna meaning "beautiful flower" is part of a list of "Girls Names From East Africa" and is NOT designated as being specifically Swahili. The Swahili part must have gotten in there when someone later ignorantly assumed that all East African names are Swahili.
It would be interesting to know where Osuntoki found the name. I doubt if he invented it or its explanation. Two pages after the list of Girls Names from East Africa is a list of "Ma-Shona" names. Several of the names on that list are also included in Jonathan Musere's _Traditional African Names_ (Scarecrow Press, 2000), with the same meanings. I think it is likely that Osuntoki did find the name Ayanna with that meaning from some African source. Though there isn't enough information in this little book to completely explain who Osuntoki was, from the introduction it seems fairly clear that he himself was a Yoruba from West Africa and so did not have direct knowledge of East Africa himself.
Personally I find tracing down where inaccurate information comes from as interesting and intellectually stimulating as figuring out which derivation is the most accurate. But of course YMMV.