To arch your back makes rotation but decreases height

[Summary]
As you can see when you jump straight, whatever you do in the air , you cannot generate rotation from jump without rotation.
If you hadn’t gotten rotation by the moment of taking off , then you cannot generate or increase in the air.
By Jumping with your back arched, the center of the gravity(CG) of your body will be deviated from the direction of pushing the ground with your legs.
In the following figures, the red crosses represent CG.

If you jump with your waist arched, the power of your pushing the ground is apt to be weaken (cf. standing front flip).
Therefore you should jump with your waist straight and instead your chest arched to shift CG after you get used to do backflip.

At the moment of taking off, the trajectory of CG is determined completely by the speed and the direction of that.
Especially, height of a flip is determined by the upward speed of that.
CG will do the parabolic motion after taking off.

[Detail and Theory]

– Rotation and Translation –

When a force is applied in the direction of CG, the object will be moved parallel to the direction of the given force.
When a force is applied to the other direction, the object will rotate.

Jumping with your back arched to shift CG ”rotation by pushing” is one way to generate rotation of two.
The other one is introduced in Tips of standing front flip. (cf. Tip2(common) : Swing your arms and upper body)
By the way, by pushing the ground, trancelation of CG and rotation is initiated together.
It can be explained with the following illustrations.

– Horizontal force + Vertical force = Oblique force –

Applying a force (whose direction is toward CG) which generates the parallel movement and a force (whose direction is vertical to the force which generates the parallel movement) which generates rotation is the same as applying  a particular oblique force.

Conversely, an oblique force being applied, the part of the force directed to CG is used to parallel movement of center of gravity and the remaining part of the force directed to rotation is used to rotate.

If the magnitude of a force is the same, allocation of the force, how much is used to move parallel or rotate , is determined by the direction of the force.
It implies that if you get more rotation, the distance CG of your body translates will gets less and vice versa.
Following figure shows a decomposed force in standing backflip.

– Translation = Height + Horizontally Moving –

You must pay attention to the fact that not all distance which CG translates is lead to the height.
The upward part is lead to the height and the horizontal part, just traveling.
Therefore, CG above the feet gives you the utmost height (but it will be difficult for you to jump with the maximum power).