Yes, Cy-Kick CS can be used outdoors to kill cluster flies. It is recommended that you apply the product in cracks and crevices where the pest may harbor or hibernate. Do not repeat applications more than twice a week. Treatments need to be done at least 3 days apart. The mixing ratio is 1-2 fl. oz. per gallon of water.
Cy-Kick CS and the Demand CS are both great products for spider control. However, neither list Brown Recluse specifically on their product label.
Transport Mikron is an insecticide you may use which is labeled specifically for Brown Recluse Spiders. Please view the full product label for more information.
Cy-kick CS is virtually odorless, and will not create a visible residue or stain when used according to the recommended label rate.