Does the three year fr-44 start from when the dui happened or from the court date?

In short, it varies based on your state and specific situation.

An FR-44 is a certificate of financial responsibility that must be filed with the state. The certificate is required by the court after certain convictions. The length of time that an FR-44 is required to be maintained may vary depending on different circumstances. An FR-44 is generally required for three years, starting on the day that the driver's license was originally suspended. However, in other cases the FR-44 is required to be in force for three years, starting from the date of conviction. If the length of time that an FR-44 is required is in question, a driver may contact their Department of Motor Vehicles for clarification. The State will not notify an insurance company that an FR-44 is no longer required. When the FR-44 is no longer mandated, it is up to the individual driver to remove the filing from their insurance coverage. If an FR-44 is removed prematurely, then the State may move to suspend the driving license in question.