Can I take the subway from Guiyang North Station to Huaguoyuan?

Of course.

According to Baidu map, walk 250 meters, get on the bus at Guiyang North Railway Station (BRT), take B7 Road (or B236 Road, B292 Road and B267 Road), pass three stops, get off at Songhua Road Station (BRT), and walk 1.0 km to reach the flower orchard. The shortest journey is about 7.8 kilometers, which takes about 34 minutes.