Simplified

--[[
    A much simplified version. The only problem with this is that wait(INTERVAL) is a blindspot.
    If the player stops during this time, and resumes really quickly,the speed won't reset.
--]]

local player = game.Players.LocalPlayer
local hum = player.Character:WaitForChild("Humanoid")

local WALK_SPEED = 16 -- Beginning walk speed
local INCREASE = 0.5 -- How much it accelerates each time
local INTERVAL = 0.1

while true do
    while hum.MoveDirection ~= Vector3.new() do -- While the humanoid hasn't stopped
        hum.WalkSpeed = hum.WalkSpeed + INCREASE
        wait(INTERVAL)
    end
    hum.WalkSpeed = WALK_SPEED
    -- Wait for player to start running agains
    hum.Running:Wait() -- or wait for hum.MoveDirection to change with hum:GetPropertyChangedSignal()
end