I know the margin around the icon is usually listed in dp (for Android at least), but let's say on a 1080p phone, does anyone know the pixel margins that would be (left edge of the screen on the left and to the bottom of the status bar on top? I'm in Sketch and it looks to be around 40ish pixels?
There is no really "standard" margin for the hamburger's margins. It depends on the design and content.
However, Google's material design guidelines (like the app you show in the question) recommends 16dp margins. The dp can be calculated using the following formula (pulled from the guidelines):
dp = (width in pixels * 160) / screen density
Ultimately it's up to the designer.