take your syringe, add 3" of tubing to the end and draw about a teaspoon/tablespoon of cleaning fluid into the syringe.
slide the printhead to an open area, place paper towel under the head.
take the damper off, place the tube on the nipple and watch under the head as you push the fluid through the head. the streams of fluid will be randomly spraying different directions, until it opens up, then they will stream straight down.
you have successfully flushed the head. put damper back on and run two cleaning cycles.