How do I prevent this code from running 6 times?

The reason why this cloning multiple instances into the limbs is because you have over 15 lines of Cloning the particle/velocity instances and parenting them.

I can start by explaining (in comments) how your for-loop is working:

--So we get the children of our character.
--This includes all scripts, humanoid and limbs.
for i,v in pairs(character:GetChildren()) do

    --Now we check if 'v' is a basepart and not a HRP. 
    --This should be 6 parts for a R6 character or 15 for R15.
    if v:IsA("BasePart") and v.Name ~= "HumanoidRootPart" then

        --You also had a redundant check for the humanoid.
        --The last if statement should of handled that.
    end
end

So this for loop should loop either 6 or 15 times if the character is either an R6 or R15 character. If you don't get that then you need to test how GetChildren() and for-loops work some more.

Now returning to the issue: You have over 15+ lines of cloning and parenting instances into each of these limb parts (End result is your image example)! You should instead remove those lines and simplify this down into two lines.

Since v should be a BasePart then this should look like:

for i,v in pairs(character:GetChildren()) do
    if v:IsA("BasePart") and v.Name ~= "HumanoidRootPart" then
        local newParticle1 = particle1:Clone()
        newParticle1.Parent = v --This clones and parents to the basepart

        local newParticle2 = particle2:Clone()
        newParticle2.Parent = v --same again

        local newDeath = death:Clone()
        newDeath.Parent = v --same

        local newVel = velocity:Clone()
        newVel.Parent = v --same


    end
end

You see how it's more readable?

Now we can clean up your full script by making some of your variables into global vars and defining services into variables.

Final Script:

--Define services. Makes it easier to read variables
local RS = game:GetService("ReplicatedStorage")
local Players = game:GetService("Players")

--That debounce wasn't needed either

--You could use WaitForChild here.
--Server side so really doesn't matter to me.
local particle1 = RS.ParticleEmitter
local particle2 = RS.ParticleEmitter2
local sound = RS.Sound
local velocity = RS.BodyVelocity
local death = RS.death
local ragdoll = RS.ragdoll

Players.PlayerAdded:Connect(function(player)
    player.CharacterAdded:Connect(function(character)
        --CharacterAdded provides you with the character
        --You don't need to set a variable for it
        --You could wait until it's loaded though!


        for i,v in pairs(character:GetChildren()) do
            if v:IsA("BasePart") and v.Name ~= "HumanoidRootPart" then
                local newParticle1 = particle1:Clone()
                newParticle1.Parent = v --This clones and parents to the basepart

                local newParticle2 = particle2:Clone()
                newParticle2.Parent = v --same again


            end
        end

        local newDeath = death:Clone()
        newDeath.Parent = character

        local newRagDoll = ragdoll:Clone()
        newRagDoll.Parent = character

        local newVel = velocity:Clone()
        newVel.Parent = character   

        local newSound = sound:Clone()
        sound.Parent = character.HumanoidRootPart --test this
    end)
end)

Edit: formatting. Fixed variable name inside of for loop in final script.