The Slot Machine is located on the first straight after the first turn.
Start an arcade race on the Beginner track (Left selection) AI difficulty, time, laps and transmission type doesnt matter but i suggest picking very easy difficulty so you can get First Place BEGINNER in Daytona USA
in the process.
Once the race begins follow the track until you get to the first straightway after the start point, there will be a 3 reel Slot Machine above the track.
Press the Button
3 times so that all 3 Slot Machine reels stop and the achievement will pop.
Here's a video demonstration