When Dragonsoul Knight’s activated ability resolves, Dragonsoul Knight will gain flying and trample in addition to its other abilities. However, becoming a Dragon will make it lose all other creature types. It will no longer be a Human or a Knight.

If Dragonsoul Knight gains flying after blockers have been declared, it won’t cause those blocks to change.

You can activate Dragonsoul Knight’s ability more than once during a turn. The second time it resolves, it will probably have no visible effect other than giving Dragonsoul Knight another +5/+3.