Is there a way to make this .gif work on GUI?

I will only give you some tips.

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1. Instead of using wait(0.05), use wait(). Since wait() is 1/30 of a second. It's the same speed that frames in a movie theater run at.
2. Do not use while loops, use RunService instead.
3. Don't use inpairs, you'll see what I do.

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Wait()

Wait() runs at 1/30th of a second. The same speed movie's frames change at. It would make the Gif run more smoothly.

print(wait()) --Prints something like: 0.031636467
print(wait(0.05)) --Prints something like: 0.0512318631

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Fun Facts about Wait

1. Like you did in your script, instead of doing while true do wait(), do while wait() do. Shortcut!

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While Loops and RunService

While loops will add lag, do not use them. Instead, use the Heartbeat event in the RunService.

while wait() do
	print("SPAM")
end
--Both run at the exact same speed.
game:GetService("RunService").Heartbeat:connect(function()
	print("SPAM")
end)

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Fun Facts about While Loops and RunService

1. While loops cause lag! RunService does not.
2. There is an event in RunService named RenderStepped. This is 2x faster than wait()! It can only be accessed with a LOCAL SCRIPT. Using this for your gif will make your gif run 2x faster, which isn't normally good...

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In Pairs

In this script, in pairs is not necessary. Do this instead:

local frame = 1

script.Parent.Image = "http://www.roblox.com/asset/?id="..frames[frame]
frame = frame+1

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Fun Facts about In Pairs

1. Instead of In Pairs, some people use next. But In Pairs should be used instead of Next.

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Final Product

Frames = {251495903,251495914,251495930,251495944,251495974} --A Table/Array doesn't NEED to be local.
local frame = 1

game:GetService("RunService").Heartbeat:connect(function()
    script.Parent.Image = "http://www.roblox.com/asset/?id="..Frames[frame]
    frame = frame+1
    if frame > #Frames then
        frame = 1
    end
end)

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Hope this helps!

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Extra

1. Use the preloader so all the gif get loaded so they aren't black.

--Add this after line 4.
game:GetService("ContentProvider"):Preload("http://www.roblox.com/asset/?id="..Frames[frame])