FlowLayout object didn't seem to recognize the change size command.
  But when I used the setColumn method, the FlowLayout object did
  respond to the change in size command. Why is this?
Form your own question i understand that you know FlowLayout works obeying component's preferred size. However to answer your question why really JTextFeild.setColumn(int) responds: Because,
As soon as setColumn(int) is called, it invalidate() the JTextFeild component and and all parents above it to be marked as needing to be laid out.
public void setColumns(int columns) {
        int oldVal = this.columns;
        if (columns < 0) {
            throw new IllegalArgumentException("columns less than zero.");
        }
        if (columns != oldVal) {
            this.columns = columns;
            invalidate(); // invalidate if column changes
        }
    }
Then while laying out, FlowLayout calls the  getPreferredSize() function of JTextFeild, which is overridden and implemented such that it returns the preferred width by adding  the column width:
public Dimension getPreferredSize() {
        Dimension size = super.getPreferredSize();
        if (columns != 0) {
            Insets insets = getInsets();
            size.width = columns * getColumnWidth() +
                insets.left + insets.right;  // changing the width
        }
        return size;
    }
Guess what! I am becoming fan of source code.