I went searching the board for posts by people who had actually done file transfers from Arduino to AI2 over BlueTooth.
I found:
This is an entirely different approach, sending the entire file character by character in a loop, and using a distinct character value that isn't going to be in the file as a completion delimiter. This changes the structure of the receiving app (at that same post) to gulping down the entire buffer and hanging until that delimiter byte arrives at the end of the transfer, at which time the full buffer text is received to allow it to be written to a file in one gulp.
There are no chunks in the sending sketch.
The author has posted many Bluetooth samples, so I imagine he knows what he is doing.
Regarding BLE, further down in that thread there is a link to an informed discussion of BLE based data transfer:
I will continue searching for line by line transfer examples.
There is an informed discussion of transfer speed at