Can you get multiple elytras after only killing the Ender Dragon once?

No, it doesn't matter how many times you kill the ender dragon. You can find an almost unlimited amount of elytra, but it is very difficult, as end cities spawn differently then other generated structures, using a random number generator to decide whether they should spawn. This is confirmed from the wiki, as it doesn't state anything about how elytra relate to the ender dragon, and from my own experience, as I have found more then five elytra by simply exploring the End for a while.