There is no proper convention, which ever method is most convenient because both methods can achieve the exact same result.
With that said, the reason why I tend to prefer having the unknown in the conical flask is because you usually have a limited supply of the unknown solution but you have an effectively unlimited supply of the standard solution. When you put something in a burette, it requires more cleaning and wastage of solution to clean it (rinse with the solution it will hold). Doing that with the standard solution is easy but it's harder to do that with the analyte because you don't have as much of it so you don't want to waste it.