Can betta fish live in distilled water?

Fairly long, at least a few weeks, due to the air breathing organ it has.

regular water changes help:

You can oxygenate the water by removing the fish and removing some of the distilled water then pour new water 4-9 inches above the tank..the higher the water the more oxygen (take into account how much water your tank hold, the less water the more splashing from a higher distance).

Next, add some soft rocks that wont affect pH (ie quartz, slate), and some betta vitamins, all this will condition the water better for the fish and keep it healthy.

Then you can put your fish back in the water, once the temperatures are the same.