1985 Regal have to blip throttle to shift from 1st to 2nd

I just bought a 1985 buick regal with 89000 miles. The body and interior were in great shape. The car drives and I drove it from the place that I bought it to my house (aproximately 85) through both city and interstate driving. I have to blip the throttle (let off)around 25 mph before the car will shift to 2nd. Once in 2nd, the car drives like normal. This is a project car that I only paid $350 for. What do you think is causing the transmission to shift like that. A friend suggested a tranny flush. I have read that it's not good t flush/change the oil in an automatic after so many miles. Please suggest what the problem might be. The car runs fine otherwise.