The amount of data transfer will depend on a number of factors. If the user is connected over WiFi, obviously data transfer is not a concern. Each user can restrict the app to connect only over WiFi, or to prompt them to confirm connection if they are not on WiFi.
That said, if they are listening over a carrier network connection, the amount of data will depend on the quality of stream supplied to the app and the how much they navigate through the features of the app since these items also require data use.
You can do the math for yourself based on the stream you have:
Bitrate in kB x 60(seconds) x 60(minutes) ÷ 1,000(kB per MB) = MB/hr of listening
Example: 128 x 60 x 60 ÷1,000 = 446 MB/hour.
Nobex Partners apps can have multiple stream formats. You can submit a higher or lower bitrate stream and the system will always supply the lower bitrate stream to users connected over carrier network to reduce data.