The only references in the constitution to installing a new president address the oath he or she must take and the date and time of the transfer of power. Everything else that takes place on inauguration day is based on the accumulation of tradition over time. The flags hanging from the Capitol’s west façade, a tradition that started at the inauguration of George H. W. Bush, is an example.
The center flag is the national flag. The two flanking it is the flag of the new president’s state (Delaware in this instance) when it joined the union. The ones on the end are the nation’s original flag.