Which of the following has no time limit for filing the appropriate Veteran's Administration application for benefits?

The marker for a veteran's grave is the correct answer because there is no time limit for filing the application for this benefit through the Veterans Administration. Families can request grave markers or medallions at any point after the veteran's death, providing flexibility for those who may not have been able to apply immediately upon passing.

In contrast, other benefits like the basic burial benefit and the plot interment allowance often come with specific deadlines for filing claims. These time constraints encourage timely administration of benefits, ensuring that the veteran's family can receive assistance during a period of grief. The flag, used to honor a deceased veteran, also follows specific filing guidelines and may have associated time limits to secure appropriate honors at funeral services. Therefore, the marker stands out as a benefit that can be requested indefinitely, allowing families the opportunity to commemorate their loved ones without the pressure of a deadline.