Acetylcholinesterase (AChE) and β-secretase (BACE-1) have become attractive therapeutic targets for Alzheimer’s disease (AD). Flavones are flavonoid derivatives with various bioactive effects, including AChE and BACE-1 inhibition. In the present work, a series of 14 flavone derivatives was synthesized in relatively high yields (35–85%). Six of the synthetic flavones (B4, B5, B6, B8, D6 and D7) had completely new structures. The AChE and BACE-1 inhibitory activities were tested, giving pIC₅₀ 3.47–4.59 (AChE) and 4.15–5.80 (BACE-1). Three compounds (B3, D5 and D6) exhibited the highest biological effects on both AChE and BACE-1. A molecular docking investigation was conducted to explain the experimental results. These molecules could be employed for further studies to discover new structures with dual action on both AChE and BACE-1 that could serve as novel therapies for AD.