The cokers I have seen do not have a minimum flow line. We did experience that problem at the coker I worked, but it was corrected by changing operating procedures.
The problem I see with a minimum flow line in this service is keeping it hot enough so that the resid won’t solidify in it.
Did you read the post from Ken Osment from Suncor on pump swap ?
Please e-mail me if I can be of any help.