The Rio Grande River forms the boundary between the US and Mexico. This brings into question what happens to that boundary if the course of the river were to change. In 1970 there were a few such disputes outstanding that the US and Mexico settled via treaty.

In addition to settling the outstanding disputes the treaty also established protocols for how to deal with future shifts in the river. For example, search for “flood” in the following document

one finds

If the Commission should determine that any of the works constructed by one of the two Contracting states in the channel of the river or within its territory causes such adverse effects on the territory of the other contracting State, the Government of the contracting state that constructed the works shall remove them or modify them and, by agreement of the commission, shall repair or compensate for the damages sustained by the other contracting state.

In practical terms, this seems to preclude building border fence in the flood plain if this may exacerbate flooding in Mexico.

The Lower Rio Grande has a flat wide floodplain and as a result, in some sections any border fence might be placed a mile or more away from the river. Land within this floodplain, whether golf courses, farms or structures are still on US soil and hence gates or gaps in the fence are added. For example this story about those living on other side of the fence.

A large difference between normal flows and flood stage poses a particular dilemma in places where floods are still a recent memory.
Presidio, Nogales, Rio Grande City and Roma are examples cited in the following article where such flooding has occurred. If future flooding occurs in such areas after additional fencing is placed, it may result in international suit.

In Texas, one legislator has filed a bill requiring flooding risks to be studied before wall construction. Though this would be an indirect effect since it would involve the State of Texas suing the Federal government.

This article describes some of the concern near Roma.