Since I don't like flanges [I think they are 'dust catchers'] and piping doesn't work as well visually on some quilts .... I Best Press all material. Then using my 1/4" flange foot add the narrow piece to the outer border. That way the borders can be added to the quilt as one piece ... again, I use my 1/4" flange foot.
I have loved the results this way. Easier to put all borders together then treat as one and join to the center portion of the quilt.
ali