You can try to measure round-trip times by having the BLE device answering that start commando, and measure the time it takes to do so (maybe doing it multiple times).
If we assume that the round time travel is equally divided between the app and the device, we should be fine but one side may cause higher latency than the other which I will never know and if altogether we have 20ms for a round trip that is split 70-30 between the devices, I won't be able to achieve 1ms accuracy.
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Well BLE is not designed for low-latency applications, but for low-power.
You can quite reliably measure latency when you use multiple packets, send from both sides, with time-stamps in them (so each side knows when the other side did send a packet, and received another one). I think NTP does something similar since it can calculate the latency between the NTP server and the client.
But it gets complicated when the delay is not constant, though.