oes anyone know what the maximum packet size is for a BLE message?

When you use GATT protocol (the only protocol currently available to the application layer) , the maximum user data in packet is 20 bytes (for example in write or writeNoResponse commands).
From tests I have made, the theoretical data rate based on calculation of 4 packets send in every connection event is not achieved in practice.
I noticed that at low connection intervals (< 100ms) the stack usually sends 3 messages per connection event (if maximum packet size is used). But as Chatto wrote, 8Kbytes/sec is achievable.