Trying to make the player take damage when function calculates the players head is on fire?

You can pass variable from one to another function.

Example:

function one()
    local number = 10 + 1
    print(two(number)) -- prints 12
end


function two(number)
    return number + 1 -- 11 + 1
end

So in your script you can do the same!

local object = script.Parent

local firePlayer = game.ReplicatedStorage.Fire

function fireTheGui(hit)
    local playersHead = hit.Parent.Head
    local player = hit.Parent.HumanoidRootPart
    local playersHealth = hit.Parent.Humanoid

    if player then
        firePlayer.Parent = playersHead
        playerDamage(playersHead, playersHealth) -- pass your variables
    end
end

object.Touched:Connect(fireTheGui)

function playerDamage(playersHead, playersHealth) -- retrieve your variables
    if playersHead.Fire then
        playersHealth:TakeDamage(2)
        print("This player is taking Damage")
    end
end

Also there's another way doing this with local function: With my understanding local function allows another function to read all non-local variables inside it.

function two()
	return num
end

local function one()
	num = 100 -- non-local variable
	print(two()) -- prints 100
end

one()

So in your script:

local object = script.Parent

local firePlayer = game.ReplicatedStorage.Fire

local function fireTheGui(hit)
    playersHead = hit.Parent.Head
    local player = hit.Parent.HumanoidRootPart
    playersHealth = hit.Parent.Humanoid

    if player then
        firePlayer.Parent = playersHead
        playerDamage() -- pass your variables
    end
end

object.Touched:Connect(fireTheGui)

function playerDamage()
    if playersHead.Fire then
        playersHealth:TakeDamage(2)
        print("This player is taking Damage")
    end
end

ALSO if you want to make the player takes damage while the fire is still on their head then do this:

function playerDamage()
    if playersHead.Fire then
        while wait() do
            playersHealth:TakeDamage(2)
            if playersHead:FindFIrstChild("Fire") == false then
                break
            end
        end
    end
end

----- OR

function playerDamage()
    if playersHead.Fire then
        repeat wait()
            playersHealth:TakeDamage(2)
        until playersHead:FindFirstChild("Fire") == false
    end
end