Kind of a random question, It has been a topic of debate in my lab. I guess the more specific question is: what materials is a fly's body made out of, and what are their dielectric properties?
You could model a fly as a chitin shell filled with blood.
Chitin is a dielectric with ε ~ 1.5 (more details here). I couldn't find the thickness of the fly's exoskeleton, though.
Blood is a poor dielectric with ε ~ 200 (fig.8 here). Note that ε is frequency-dependent.
Relative permittivity of blood/muscle is close to the one of water, and depends strongly on the frequency, as can be seen in the excellent "vintage" MIL document referenced by Nick (thank you for that). Permittivity of Chtitin is much lower than of water but I think the value given is too low. I would guestimate permittivity at 2-3, also frequency dependent, but not as heavily as water. And the dielecttric losses would be lower too. So basically if you want to estimate the permitivity of a fly or basically any arthropod, take 30-50% of its weight to be water or blood, and this will be the main contribution to its total permittivity. Have fun!