Are they on our DJI account, in the "cloud" or are they stored locally on whatever disk or tablet we use to fly?
If I delete & reinstall DJI Go will I lose my logs?
The raw log data is stored internally on your Phantom. I don't think DJI ever deletes that data, but I suppose the oldest logs will be overwritten by newer logs when there is no more storage available. See more about those logs here.