That would be about 6000 square feet; with drip, you might be able to get by with about 1/2″ per week during dry periods. That would be about 400 cubic feet, about 3000 gal, per week. Here in central Texas, our about 35″ of rain will support un-irrigated berries. Some dry years, they may need irrigation to get established between February and July. Once established, the crop may suffer in dry years, but the planting will not likely die.
Typical crops need about 1″ a week in hot dry weather. Your blackberries are likely to be in rows 10′ apart, occupying 2x300x10=6000 square feet. With drip, you might get away with half the “needed” water by avoiding watering the weeds in the middles. Therefore, 1/2″, but all applied in the rows of blackberries. Or, 1″ over half the area. 1/2″ over 6000 sqft or 1″ over 3000 sqft. Same thing, depending on how you think about it.
The water holding capacity of your soil might allow you to water infrequently, but (in hot dry weather) your crops will be trying to get around 1″ a week; your plants will probably do best if they get irrigated once or twice a week (1/2″ or 1″ each time), but you might get away with once in two or even three weeks (2″ or 3″ each time). My established blackberries will go through a month of hot dry weather before they draw the stored water in the soil down enough that they start suffering. “Established” just means that the roots can draw water from 18″-24″ deep.