I have read the "Building constructs" section and wonder if it is possible to add fly speed to a golem.
Damn golem is immune to magic, so no fly spells, i dont know if "wings of flying" item can be attached to a golem (more like jetpack of flying).
One can make a delving property into an armor of the golem, but that is burrow speed. There is no similar flying one as far as i know.
Golems are immune to magic as a finished product, they still fall under the " item creation " concepts. Personally, it would all depend on what Golem your looking to have fly. Though I wouldn't think that it would be such a big issue to add a fly speed, just pay attention to the maneuverability.
It will look like Gundam robot and yea, it will be clumsy as hell.
There was an iron golem that could either fly or had air walk in Runelords. It also fired energy bolts.
So, basically, do whatever you want; just keep the CR in mind.
Is this a golurk? Is its legs and hands going to withdraw, giving off rocket blasts?