Is it normal to have heart palpitations that is relived by burping while having the flu? I've had chills with no fever at night as well.

Influenza. If you have influenza as diagnosed by specific testing, this is a recognised cause of myocarditis, and can lead to significant impairment of cardiac function and mortality. Other viral causes of an influenza-like illness can also be responsible for cardiomyopathy. Strongly suggest you see a doctor and get fully evaluated and tested. Good news is that complete recovery is the rule. Good luck.