As far as I have learned 私は行っている can't mean something like "I am going", but would mean something like "I am going regularly (for a certain time)" or "I went there and am there right now".
I have also learned that you can use てくる after a verb like なる to indicate that a change has started in the past is happening right now and will continue happening in the future for some time.
Therefore it seems to me that 行ってくる would be the best Japanese substitute for the English "I am going". I am however not certain what kind of verbs てくる can be used with. My questions therefore are:
Can I use てくる with 行く to convey the meaning of "I am going" and if not how can you convey the meaning of "I am going"?
When in the timely context of てくる (or ていく for that matter), where lie the boundaries of the verbs with which you can use it?