Can amlodipine besylate cause any problems for someone who has occassional episodes of atrial tacky? Is it a safe drug?

Anti hypertensive. Amlodipine is a commonly used anti hypertensive medication. It has no significant effect on atrial tachycardia.
No. Amlodipine doesn't affect the heart rate in any way. So it won't slow down your heart rate. It won't make the tachycardia worse either. However, it won't be treatment for it. There are some other medications for hypertension that can control tachycardia as well. Those will have to be evaluated by your provider to determine if they are appropriate for you.