>>39432924GF chooses Megas based on game balance, a Pokemon's popularity, and whether it makes sense in universe for a Pokemon to get a Mega. Audino had all 3.
Game balance - There aren't too many Normal-type Megas, and no Gen V megas, so Game Freak chose Audino.
Popularity - Audino is fairly popular in Japan due to its cutesy design. Furthermore, GF assumes Audino is popular through web searches and online videos, but this was largely because Audino was the easiest way to get EXP in the Gen v games.
Reason for lore - Audino has three main themes. First, it has those large ears with curly ends that resemble part of a stethoscope. Second, Audino has that pink color pattern on its stomach and arms resembling an open doctor or nurse's jacket. In these two aspects, Audino resembles a doctor. Audino heals itself and other Pokemon, so it has that as a theme. Third, Audino has a pun with its name (Tabunne is tabu [ear] plus ne [maybe]), a hint that this Pokemon does not have a definitive encounter ratio in the games. In Gen V, you had to search it out via phenomenon, but in most locations it is not a guarantee you'll find out (especially later in the games). In Gen VI, Audino are found in bushes but only at a 20% encounter rate. A bush randomly shakes when you pass by Route 6, and you are not guaranteed to get an Audino out of it. They are also found in a Friend Safari, another place where you are not guaranteed to get one. In ORAS, Audino are found on a Mirage Island, another inconclusive location. And in USUM, it is found in Ultra Wormholes, another place where the encounter is a maybe and not a definite. For Megas, only SOME Pokemon get them, so it is indeed a maybe factor. So this maybeness works for Audino, as it may get a Mega but not guaranteed to get one (which was why it got one in ORAS). And Audino gets the dormant power of its healing abilities awakened as a Mega, where it can heal others more effectively.
