Can I jump while flying?

Question

Assume we have a character who has a natural fly speed and a class ability that heavily benefits them to jump (with an Acrobatics check)¹. Assume they are flying, say 20' above an open field with enemies at various distances both in the air and on the ground.

The confusion comes from the idea that physically we think of jumping as "off of something", while the rules don't actually state this. Additionally, we can imagine a flying creature flapping heavily or some such thing for a jump-like effect through the air.

Could this character make an Acrobatics check to jump whilst they are off the ground flying?

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1: The class ability is 3pp that allows use of Vital Strike with extra bonuses at the end of a jump as a full-round action, but otherwise says it functions as an acrobatics check to jump.

Answer 1

After a careful reading of the acrobatics skill and the jumping subsection it would indicate that NO, you are not able to jump while flying.

My reasoning for this is two things. First, you are flying and there is a complicated rules section to deal with everything flying, and it does not mention jumping. Second, all language in the jumping rules section refers to base land speed, or surfaces jumped from (which while flying you dont actually have a surface), which implies that its not usable with other movement speeds.

Take a look at another special condition, charge. When taking about movement speed it clearly does not mention land speed or any movement type. This makes it possible to charge while flying (also swimming and burrowing...).

Answer 2

Jumping by definition requires a surface to push off of. The Pathfinder SRD seems to support this with this section on Acrobatics checks and jumping (emphasis mine)

The only Acrobatics modifiers that apply are those concerning the surface you are jumping from.

However, the Fly skill is used to handle complex maneuvers while flying

From Pathfinder SRD:

You are skilled at flying, either through the use of wings or magic, and you can perform daring or complex maneuvers while airborne. Note that this skill does not give you the ability to fly.

Since the 3pp class ability requires an acrobatics check for jumping, why not change the check to a Fly check instead of an Acrobatics check?