Why do all fighter jets and aerobatic airplanes have flat wings? According to Bernoulli's principle and for a given angle of attack would that not lower the lift force of the airplane and increase its drag and therefore increasing its demand in thrust and fuel consumption?
This is anti-economic and puts the airplane under unnecessary mechanical stress.
I am not referring to the angle of attack adjusted by the pilot during flight or to any preinstalled by the manufacturer angle of incidence on the wings to support lift but solely to the shape of the wings. For example aerobatic airplanes (i.e. stunt planes) and most modern fighter jets, they don't rely at all on wing shape for lift. Their wings are evenly shaped flat upside and downside (i.e. instead of being usually in other airplanes, curved upside and flat downside).
Therefore, their flat evenly shaped wings do not support additionally to the angle of attack and incidence angle the lift of the plane.
Why not this additional feature of upside curved wing shape is not present in this kind of airplanes? Is there any particular reason(s)?
What is the trade-off here? A curved wing creates lower resistance on the upside and therefore faster air speed and lower air pressure (Bernoulli's principle) upside. Thus, increases lift in addition to the main lift generated by the angle of attack and incidence angle.
It would be logical to make use of this feature in fighter jets and aerobatic airplanes to generate larger lift with less thrust and less fuel consumption.
 A: The "equal-time fallacy" is alive and kicking, as shown in your question and the other answers. Look, here is the best explanation I've seen about how wings work and airplanes fly: https://www.av8n.com/how/
The "equal-time fallacy" says when two molecules of air get separated at the leading edge of a wing, they must come together at the trailing edge. So in order to get faster flow over the top (for lift), there must be a longer curve over the top. WRONG. The molecules do NOT meet up. The upper one gets there first. The result is a vortex in which air is pushed DOWN, and that makes the lift.
Wings lift because they push the air down, not because they are shaped a particular way, but because they fly at an angle-of-attack (AOA). The shape is just an optimization for typical flight. Wings on aerobatic airplanes are symmetrical because they typically fly inverted just as well as upright.
Is Bernoulli wrong? No. Bernoulli is absolutely true. What is wrong is the typical explanation, which is still being taught to kids. Again, read https://www.av8n.com/how/
A: 
For example aerobatic airplanes (i.e. stunt planes) and most modern
fighter jets, they don't rely at all on wing shape for lift. Their
wings are evenly shaped flat upside and downside (i.e. instead of
being usually in other airplanes, curved upside and flat downside).

Symmetrical wings still rely on their curved shape for lift, but need a positive angle of attack to produce it. A symmetrical shape has the advantage that the wing produces the same lift whether it is right way up or inverted, which is important for good aerobatic handling.
The lift of any wing increases with airspeed, but so does drag. A thicker wing produces more lift, but also more drag. An aircraft designed for high speed needs a thin wing to keep drag down, and doesn't need camber because it can produce enough lift without it. However when taking off and landing it may need camber to produce enough lift at low speed, thus the reason for flaps.
A truly flat wing is inefficient because without a curved shape to follow the air 'unsticks' from the top surface and turbulates as it goes over it, increasing drag and reducing lift. But the bottom surface still produces lift so it still functions as a wing, just poorly. Model aircraft are sometimes made out of thin flat sheets of balsa or polystyrene foam for easy construction. They have poor efficiency, but this doesn't matter because fuel economy is not an issue.
A: 
Is there any particular reason(s)?

There are actually two reasons.
Fighter jets are designed to fly at supersonic speed. Airfoil camber (that is the proper name you were looking for) helps at subsonic speed to make lift creation more efficient, but is a source of drag (wave drag) at supersonic speed. Fighter wings have very little relative thickness and little camber in order to reduce wave drag.
When those fighter wings need to produce lots of lift (which happens either at take-off and landing, or in maneuvering around Mach 0.7), they rely on vortex lift which is caused by flow separation at the leading edge of a swept wing. With separated flow, the details of the wing's contour don't count anymore, so camber is again not needed in fighter wings when high lift is required.
Aerobatic planes do away with camber completely, and for a different reason. It is much easier to fly rolls with an uncambered wing. The main advantage is less in inverted flight per se but in the transition between upright and inverted flight. This answer gives you the details.
A: Fighter jets should be fast (> Mach 1), fast rolling and small flight curve for fast turning (good manoeuvrability). For > Mach 1 it is of advantage, in regard to good manoeuvrability (M < 1) as well. Nobody cares about the economical aspects and yes higher stress, but if better manoeuvrability than the other fighter is given, this is taken into account. Utmost object for those fighters is manoeuvrability and speed, so they have to design it on the instability limit of a flight process (in flighter jets a pilot couldn't handle it, the basic stability is controlled by the electronic system) and material strength.
