Is It Ok to Do Chest Exercise While Having Gynecomastia?

Gynecomastia is composed of fatty tissue and glandular tissue.The fatty tissue can be altered by diet and exercise; however, the glandular tissue will not be affected.  Exercise will help with the development of the pectoralis in terms of making it more bulky or enhancing its definition.  This will not alter gynecomastia except pushing it more outward.

If for some reason you feel surgery isn’t right for you, you may wish to consider non-surgical options. For example, a good diet and sufficient exercise will also be helpful in lowering your overall body fat percentage.
Gynecomastia is excess breast tissue, not fat tissue. That means exercise won't have a major impact on it.  Even things like exercises specifically for chest may not make any difference.
To sum it up, a clean diet and a good workout routine will be helpful but it may not always be enough, surgery may still be required to remove the glandular element.