Based on the information you provided the Soldier cannot be flagged nor could they be tested for the 2nd for record test.
There must be at least four months separation between for record APFT. AR 350-1 states:
G-9m(2) Commanders may administer the APFT as often as they wish; however, they must specify beforehand when the results are for record. AA and AGR Soldiers will take the APFT twice each calendar year. A minimum of 4 months will separate record tests. Soldiers that require make-up testing or re-testing for an APFT failure are exempt from the 4-month rule. The intent is for the Active Army and the AGR Soldiers to take a record APFT every 6 months. Mission requirements often prevent the even spacing of record tests. Therefore, commanders are encouraged to test Soldiers for record as close to the record test window as possible. Soldiers requiring make-up testing will be scheduled in accordance with the unit Standard Operating Procedures. Soldiers requiring re-testing for an APFT failure will be scheduled as prescribed in paragraph G–9.m.(6) of this regulation.