One way to fix an overflow of a Text Widget within a row if for example a chat message can be one really long line. You can create a Container and a BoxConstraint with a maxWidth in it.
Container(
constraints: BoxConstraints(maxWidth: 200),
child: Text(
(chatName == null) ? " ": chatName,
style: TextStyle(
fontWeight: FontWeight.w400,
color: Colors.black87,
fontSize: 17.0),
)
),