Hi JustPlaneD,
What you are asking for is really quite unique. I personally don't know of any products / software that would let you:
Log serial data to microSD file
Periodically close the file and open a new one
At random points in time, allow a BLE connection from an App / application
List (provide a directory of) the microSD files
Allow selection of a single file
Echo its contents to the application over BLE
Have the application save the data to file
The "OLA" code and application need to be able to work together to list the files and transfer a single file. You'd need to put development work into the application too, not just the OLA BLE functionality.
It would be more straightforward to echo (broadcast) the serial data to BLE, like a Serial terminal / monitor, and have an Android App like "Serial Bluetooth Terminal" save the data. If you can avoid the list-and-select-file features described above, and limit yourself to a single file, it becomes much more achievable:
Log serial data to a single microSD file
At random points in time, allow a BLE connection from an App / application
Echo the entire file contents to the application over BLE
Have the application save the data to file
I'm pretty sure you could get something working there, using Android Serial Bluetooth Terminal as the App. Not with OLA, but ESP32 could certainly do it.
How much data do you need to log? I wonder if you could also do this using a Dynamic RFID tag? This one -
https://www.sparkfun.com/products/21274 - can store up to 8kBytes of data which can be read using a mobile phone App. You write data to the tag over I2C in a format which the App can read and save. The App can delete the data too once read.
I hope this helps,
Paul