Need help with attaching wood to cinder block
Use a hammer drill with a 5/32" masonry drill bit to install 3/16" Tapcon phillips concrete anchors that are 1-3/4" long. The phillips head should countersink itself flush as you drive it into the furring strip. You may need to use a countersink drill bit before driving the Tapcon to help it sit flush depending on the hardness of the furring strip.