How do I rotate an object inside of a GUI?

All GuiObjects have a Rotation Property. You can increment this Property in a numerical for loop to make a spin animation.

local guiObject = script.Parent --Object to rotate
local incr = 1;

for i = 1,360 do
    guiObject.Rotation = guiObject.Rotation + incr
    wait()
end

If you want to continue this animation for 30 seconds, you can use the tick function to decide how much time has passed.

local guiObject = script.Parent --Object to rotate
local incr = 1
local Then = tick() --Time before it started rotating
local limit = 30  --Amount of time it should spin

while Then - tick() < limit do --Only animate within time limit
    for i = 1,360 do
        guiObject.Rotation = guiObject.Rotation + incr
        wait()
    end
end