It is neither unique nor common for a national or state/provincial/territorial flag to feature a tree (or a portion). Lebanon and Canada come to mind for nations with the Cedar Tree and Maple Leaf represented. The US state of South Carolina includes a Palm Tree.
Today we’re going further South than the United States. And we’ll include many miles West — to the other side of the International Date Line. On a white background, between vertical bars of green, the Norfolk Pine is depicted on the flag for the Territory of Norfolk Island. I don’t know about your geography expertise, but I needed to consult an atlas to find this external territory of Australia. (It’s located 877 miles due east of Australia and northwest of New Zealand’s North Island)
This is the home of the Norfolk Island Pine. The tree has become a popular evergreen ornamental world wide. In its natural habitat it can reach a height of 200 feet. In other climates, and when grown in a tub (best method in St. Louis) it obtains a more most stature of 3-6 feet. A long lived ornamental it adds a welcome bit of green contrast to the browns of a Midwest winter.