Why can't i make this move have a cooldown(i'm using a bool value and a local script)?

Lots of errors in your scripts.

First, In line 2, you changed line 1 from an object to a boolean. So Say cf.Value = true on line 2.

Next, In your “onKeyDown” function you have lots of errors. I won’t even list them. Learn coding. So do more research.

Then, Mouse.KeyDown is deprecated. So switch to ContextActionService or UserInputService.

Finally, You didn’t make the "f" in findFirstChild an uppercase. Not findFirstChild You should Take case sensitivity into consideration. If you can’t spell, don’t even script.

local canFire = script.CanFire
canFire.Value = true

local disappear = 0.5
local dmg = 50
local key = Enum.KeyCode.Q
local speed = 500

local plr = game:GetService('Players').LocalPlayer
local char = plr.Character or plr.CharacterAdded:Wait()

function fire() 
    local ffa = char.Humanoid:LoadAnimation(script.FFA)
    ffa:Play()
    wait(1)
    local x = Instance.new("Part",game.Workspace")
    x.TopSurface = Enum.SurfaceType.Smooth
    x.BottomSurface = Enum.SurfaceType.Smooth
    x.Shape = Enum.PartType.Ball
    x.Transparency = .5
    x.Size = game:GetService("ReplicatedStorage").x1.Size
    x.BrickColor = BrickColor.new"Bright red"
    
    local f = Instance.new("ParticleEmitter", x)
    f.Texture = "rbxassetid://410256160"
    f.Rate = 300
    f.Size = game:GetService("ReplicatedStorage").Meraf.Size
    
    local y = Instance.new("BodyVelocity", x)
    y.Velocity = Vector3.new(char.Torso.CFrame.lookVector * speed)
    y.MaxForce = Vector3.new( math.huge, math.huge, math.huge )
    x.CFrame = char.Torso.CFrame * CFrame.new(0, 0, -12)
    
    local dmgScript = script.DmgScript:Clone() — I will make the dmgscript later. Make sure it’s Disabled property is set to true
    dmgScript.Parent = x
    dmgScript.Disabled = false
end

game:GetService("ContextActionService"):BindAction(“Fire”, fire, false, key)

Now for the dmgScript. Yes they must be different scripts. Make sure its Disabled property is set to true. The above script will set it to false so it can work.

local cf = script.Parent.CanFire — this script is inside the localscript 

script.Parent.Touched:Connect(function(part)
    local hum = part.Parent:FindFirstChild("Humanoid")

    if hum then
        hum:TakeDamage(50)
        
        wait(1) 
        script.Parent:Destroy()
        cf.Value = false
        wait(3)
        cf.Value = true
    end
end)