What range in energy flux corresponds to this magnitude range?

Equate (Sun's) insolation which is 1370 W/m² with Sun's apparent magnitude.
An upward figure (moving positive from this figure) of magnitude 5 indicates a hundredth of the energy flux (I am not going to calculate atmospheric absorptin & other effects; but these are to be taken in).
For energy flux things like absorption (factor), dilution by inverse square law while travelling, may need to be multiplied. The magnitude scale offers easy computation by adding these (instead of multiplying) as equivalent indices (to the radix 2.512 which is nothing but 10^0.4).
Magnitude scale operates in a negative way. You must be cautious about that. The more negative it is the greater the energy flux. It is necessary to put a minus (-) before magnitude figure before entering into a computation, notionally holding magn.0 as reference.

You asked about the range magn.6 to magn.-27 (of Sun)
6 -(-27)= 33.
The range spans 33 on magn scale starting from magn.6 to -27; that is
(2.512)^33
 = 10^[33 X 0.4]
 = 10^13.2 =  1.585 X 10¹³.
Sun is brighter so many times of magn.6 star.
That is, magn.6 star is dimmer by a factor
1/1.585 X 10¹³ = 0.63 X 10?¹³, which when multiplied by 1370 W/m² gives
8.644 X 10?¹¹W/m².
So the range of flux is 1370(for Sun, magn.-27) to 8.644 X 10?¹¹W/m²(magn.6)
1/2.512 X 10²
 = 3.9810