How could i make my FP arms smoothly slide into position, rather than roughly teleporting?

Here, you can TweenService, although you have created variables but haven't used it.

Here, we are gonna a new local function for Tween..

-- Setting up variables ..
ArmsV.Value = Arms.PrimaryPart.CFrame

-- If there is blue dash below ArmsV.Value, try making it 'local'.

local function TweenPlayer(object, tween, properties)
    local TweenService = game:GetService("TweenService")
    local TweenInfo = TweenInfo.new(tween, Enum.EasingStyle.Linear, Enum.EasingDirection.In, 0, false, 0)
    local Tween = TweenService:Create(object, TweenInfo, properties)
    Tween:Play()
    return Tween
end

Now to run your Tween, you can simply do:

-- Add Cframe change detecter

ArmsV.Changed:Connect(function(value)
    Arms:SetPrimaryPartCFrame(value)
end)

-- Triggering the TweenPlayer function
TweenPlayer(ArmsV, 3, CFrame.new(0, -1.2, 0.3)

Setting up above things in your script..

local Camera = workspace.CurrentCamera
local RunService = game:GetService("RunService")
local CharacterBodyColor = Character:WaitForChild("Body Colors")
local ArmBodyColor = Arms:WaitForChild("Body Colors")
local Humanoid = Character:FindFirstChildOfClass("Humanoid")
local Clothing = Character:FindFirstChild("Shirt"):Clone()
local CanTrack = true

Arms.Name = "Arms"
ArmsV.Value = Arms.PrimaryPart.CFrame

-- If there is blue dash below ArmsV.Value, try making it 'local'.

local function TweenPlayer(object, tween, properties)
    local TweenService = game:GetService("TweenService")
    local TweenInfo = TweenInfo.new(tween, Enum.EasingStyle.Linear, Enum.EasingDirection.In, 0, false, 0)
    local Tween = TweenService:Create(object, TweenInfo, properties)
    Tween:Play()
    return Tween
end

--[[ local function assignArms()
    if CanTrack == true then
        Arms:SetPrimaryPartCFrame(Camera.CFrame * CFrame.new(0,-1.2,0.3))
    end
end ]] --

ArmsV.Changed:Connect(function(value)
    Arms:SetPrimaryPartCFrame(value)
end)

local function deleteArms()
    Arms:Destroy()
    CanTrack = false
end

local function adjustArms()
ArmBodyColor.LeftArmColor3 = CharacterBodyColor.LeftArmColor3
ArmBodyColor.RightArmColor3 = CharacterBodyColor.RightArmColor3
Clothing.Parent = Arms
end

Arms.Parent = Camera

adjustArms()

Humanoid.Died:Connect(deleteArms)

RunService.Heartbeat:Connect(TweenPlayer(ArmsV, 3, CFrame.new(0, -1.2, 0.3))

Lemme know if it helps!