During the Chrell Invasion, Floyd Lawton joined S.H.I.E.L.D. and worked as an agent, fighting against the Chrell. While the war waged on all around, it actually worked to cure the mental instability that he had, giving him a different perspective on the nihilism that he had previously espoused. Unfortunately, this change in philosophy was not going to work too long for him, as he was sidelined with a serious injury.
While the injury made it impossible for him to ever be in the field again, he decided to use his knowledge to create a private military corporation aptly named after his field alias, Deadshot. He decided to work on training mercenaries and assassins, teaching them everything that he knew. He wrote down a series of rules, regulations that this organization would use.
Over time the organization has grown in number and in reputation, and has continued on, despite Lawton’s death. Deadshot Inc. takes almost any and all contracts that come their way, and spare no expense in ensuring that the contracts are fulfilled, to the letter. Every operative, once fully trained, is considered to be a “Deadshot”. Each Deadshot is granted some operational leeway when it comes to picking and choosing their contracts, but if there is a particular target that the higher ups want a Deadshot to take care of, then that trumps their individual freedom.
This grants the organization a large amount of freedom, as there is no one single "Deadshot". Furthermore, it allows them to diversify where they work around the globe, and have specialized operatives in the different countries or regions. Each operative is only given a certain amount of information on the overall organization.
Mors venit velociter ("Death comes quickly")
Gotham Deadshot (deceased)
Deadshot (Suicide Squad)