[jcwade]

Any naval battles in the Coliseum would have been soon after it opened in 79 AD.
Afterwards, there were halls and ramps and cages built to hold the animals, gladiators and support people. These below ground structures would not have allowed it to be flooded. You can still see them today when you go to Rome.

Naval battles would have been held at nearby lakes. These had the advantage of being larger, for more mobility and deeper for better drowning.

Interestingly, the Coliseum was known as the Flavian Ampitheatre after the dynasty that built it.
It took the name of Coliseum because of the colossal statue of Nero that stood nearby.