For lists of letters, the easy accepted informal way is to just say out the letter names in order.
Over a poor communication medium, like a bad cellphone, sometimes letters get confused. So there is a pattern of saying, as you say, a letter followed by a word that starts with that letter.
Informally, there is no general corresponding set of words to letters, one just picks one at random. A common way to say it is:
A as in Apple, B as in Boy
(patterned after children's alphabet learning books).
There is a tendency to use people's names though, for example:
A as in Adam, B as in Barbara, C as in Charles...
(notice that the sound doesn't have to match)
But that's informally. In formal situations, like the military, there is a prescribed mapping of letters to words:
A as in Alpha, B as in Bravo, C as in Charlie
This is the NATO phonetic chart. (there are others but this is the most widely used in the US).
Your question seems to focus on vowels, but in these methods there is nothing special about vowels.