This is very variable. An estimate may be given by the manufacturer but it is very dependent on the environmental conditions at the time. The length of time that the vest stays cool will be affected by the humidity, air temperature, sunlight strength, dog breed and activity levels.
Most vests can stay wet for up to five hours in ideal conditions but it can be a lot less. Don’t forget that you can ‘reset’ an evaporative vest by wetting it again with a hose-pipe or with water from a stream.