EditBox control elements offer a copy to clipboard method.
You can either use an existing editbox like the chat input box or create your own, set the text and then call the copy function.
Code:
-- do this once
local clipBoardControl = WINDOW_MANAGER:CreateControl("Chat2ClipboardControl", GuiRoot, CT_EDITBOX)
clipBoardControl:SetHidden(true)
clipBoardControl:SetMaxInputChars(1000)
-- call this whenever you want to copy something
clipBoardControl:SetText("Hello World")
clipBoardControl:CopyAllTextToClipboard()