‘Defacing’ is the proper term in vexillology.

From the Wikipedia article on the term:

In vexillology, defacement is the addition of a symbol or charge to a flag. For example, the Australian flag is the British Blue Ensign defaced with a Southern Cross in the fly.

In the context of vexillology, the word “deface” carries no negative connotations, in contrast to general usage. It simply indicates a differentiation of the flag from that of another owner by addition of elements. For example, many state flags are formed by defacing the national flag with a coat of arms.