I have a fluttering in my stomach. It is similar to the feeling of a baby's early kicks. I also have occassional eye flutters. Any ideas?

Probably unrelated. Eyelid fluttering (twitching) is a common happening in young adults due to nerve hyperactivity. It is benign and should be ignored unless it is so prominent and happens so often that others notice it. Stomach fluttering probably is the same process in the abdominal wall. It is hard to sort out actual stomach motion from that of other intestinal organs.
Eyelid spasms. Eye flutters known as blepharospasm are benign and are equivalent to a facial muscle twitch. Stress, excessive caffeine intake and vitamin deficiencies can lead to them. There are also more significant twitches including hemifacial spasm. If you're entire face or half of your face is having muscle spasms, then seek medical care as it could be indicative of an underlying medical condition.