The combustion chamber efficiency in many modern gas turbine is about 98~99 %.
in theory, based on its input and output and also fuel flow consumption, you can calculate its/their efficiency. However, in practice, it is impossible ! because there is no sensor at its/ their outlet !
The first law efficiency of a GT combustion chamber is really high at it is related to the abiltity to convert approximately 100% of the chemical energy of the fuel. Considering that in a well operating combustion chamber the emissions of UHC and CO must be particularly reduced (ppm or similar level) it is evident that the efficiency is very close to 1.
However, if we consider second law efficiency the situation is different since the combustion process is one with very high ireversibilities since a fisrt kind energy (chemical one) is trasnformed in a second kind one (the heat) and therefore the capability to generate useful work (exergy) is reduced if compared to the original exergy content in the fuel. Considering that due to the need of TIT reduction compared to flame temperature for GT materials constraints obtained through tertiary air in the combustion chamber irreversibilities are high and second law efficiency is not so high.
This is the reason why the use of fuel cells where the fuel is electrochemically converted (not burned) in a very well organised and reversible way is more efficient than any combustion process.
It depends on different factors. you can compare the actual cycle with the Carnot cycle efficiency. You can write a suitable code in EES software to this purpose.