Audio messaging is a relatively new technique as far as mass consumer adoption is concerned.
I am unable yet to find any good publicly available statistics regarding the extent and growth of audio messaging. However a lot can be deduced by looking at the growth of messaging apps, smart phones, and the percentage of time using these features.
As of 2/20/2014 WhatsApp users were sending 200 million voice messages a month - as compared to 1200 million text messages - expandedramblings.com 
As of early 2014, an average user shares about 40 pictures, 7 videos and 13 voice notes per month on WhatsApp.
There are now more messaging users than social media users globally - slideshare.net
We now spend more time in messenger apps than we do on social media. It’s reported that over 2.5 billion people have at least one messaging app installed. By 2018, Activate Forecasts that number to grow to 3.6 billion people - atchai.com
# Text messaging
According to Flurry, a market-research firm, the total number of text messaging users grew by more than 100% in 2015, which explains why old-style text messages seem to have peaked - economist
Together the ten biggest messaging apps, which include KakaoTalk, Viber and WeChat, now boast more than 3 billion users.
WhatsApp, the leader of the pack, alone has 700m—a big reason why Facebook last year paid $22 billion for the firm, despite continuing to develop its own Messenger app - March 2015
As the number of users has grown, specialised versions of messaging apps have emerged. What made Snapchat popular was the ability to exchange pictures that vanish after a few seconds (and often contain nudity). Secret, Whisper and Yik Yak let users remain anonymous (including bullies, unfortunately).
Telegram stands out because of its strong encryption (making intelligence services unhappy). And FireChat works without cellular service: users’ phones communicate directly, which was a popular feature during recent protests in Hong Kong.
The time users are spending on messaging services has encouraged investors to value them highly, even though it is not yet clear how some of them will make money—much as happened with the rise of Twitter and with Facebook’s original service, its social network. WhatsApp handled more than seven trillion messages last year, about 1,000 per person on the planet. In Britain users spent as much time on WhatsApp as on Facebook’s social-networking app, according to Forrester, another research firm. In China subscribers to WeChat are estimated to use the app for about 1,100 minutes a month on average.
Although the numbers are smaller, something similar is happening in the business world. Slack, a messaging service that works on both smartphones and personal computers, seems to be succeeding where other attempts to create “corporate social networks” have failed, by replacing e-mail as the main communications channel inside firms. Just over a year old, Slack now has 500,000 users. It says they typically spend 135 minutes each working day on the service and altogether send 300m messages a month—which is why investors valued the firm at more than $1 billion when it raised capital in October.
We now spend more time in messenger apps than we do on social media. It’s reported that over 2.5 billion people have at least one messaging app installed. By 2018, Activate Forecasts that number to grow to 3.6 billion people.