HI, thanks for using healthcare magic
It is understandable to be worried about the possibility of 
heart disease since there is a family history but though your father had similar burping episodes, this particular symptom is not likely related to heart disease.
Heart disease presents with 
chest pain in the central chest. This chest pain is normally crushing,tight or heavy. It comes with activity and decreases with rest. It is associated with 
shortness of breath, palpitations and excess sweating.
Burping comes from the gastrointestinal tract not the cardiovascular system. It may indicate that you have reflux or intolerance to some foods.
The fluttering may be related to the heart, it may signify palpitations but this can be confirmed by your doctor who would likely suggest an ECG to look at the rate and rhythm of the heart.
A healthy lifestyle can decrease your risk of heart disease.
This means maintaining a normal weight, exercise, healthy diet, no 
smoking, checking 
cholesterol.
If your cholesterol is high, it should be treated.
I hope this helps