I am not sure I follow what you have done.
To calculate the instrument response using a MILES star, you take a spectrum of the actual MILES star you have chosen, not one which happens to have the same spectral class. (The actual spectral class does not matter as long as it is a hot star, it is probably unreliable anyway!) That way you end up with a spectrum of the MILES star as measured with your equipment which you can directly compare with the one of the same star in the library, which was measured and calibrated by a professional. The ratio of the two is your instrument response.
You can then use this instrument response to correct a spectrum of any target measured using your setup, (even if you have no idea what the spectrum will look like) to produce a fully calibrated spectrum. (With one caveat – you should chose a MILES reference star at similar altitude to your target so the effect of atmospheric extinction is the same.)