Does a heart flutter mean heart problems?

Not necessarily: Fluttering in the chest, depending on one's sensitivity, may reflect some irregularity in the heart rhythm. Those may be normal for any given person, but indeed may be a harbinger of something more serious. Discussing this with your doctor will allow your doctor to get some tests (ecg, holter or event monitor, possibly an echocardiogram and/or stress test, and blood work) to sort this out.

Not necessarily: But if bothersome or lasting more than a couple of seconds further evaluation may be warranted as this could be many things.