How do you convert an observed magnitude to a flux? For a series of supernovae I have the observed magnitude and I want to convert these values to flux.

I understand that I need to apply:

$m - M_r = -2.5\log_{10} \frac{F}{F_r}$

where $M_r$ is a 'reference magnitude' with corresponding known 'reference flux'.

What exactly should I use as my reference values?
The reference magnitude and flux really depends on what filter (i.e. range of wavelengths) the observation was made at (e.g., see the UBV system, or a more complete set of photometric passbands here). If you know the filter, and it is in one of the common ultraviolet, optical, or near infrared filters, then this website and this website provide useful reference fluxes. Using the common AB magnitude system then a source with a measured magnitude of zero in any band by definition has a reference flux of 3631 Jy (where 1 Jansky = 10-26 W Hz-1 m-2).