Thanks for the D2D. It is wise to consult both an Orthodontist and a Periodontist before treatment is started so both specialists are in agreement with the treatment plan.
Usually, braces (Orthodontic treatment) is done first as it is sometimes possible to intrude the teeth with braces and reduce the height of gum display.
Also, if braces are done first, sometimes we need to remove less bone and gums during gummy smile surgery. Also, the gums levels will move during braces so it would be much better to level off the gums when the teeth have stopped shifting and are in their final position.
So in general, it is better to do braces first before gum surgery! Although there are exceptions to the rule.