Is there a way to use an animation in the game for free?

Please, paying robux for an animation is boring.

Well you can use :LoadAnimation or you can make your own. I will give you a frontflip and backflip localscript. Put it in your StarterGui(remember it's a localscript) press q for backflip and press e for frontflip:

while wait() do
	if game.Players.LocalPlayer.Character then
		break
	end
end
mp = game.Players.LocalPlayer
mpc = mp.Character
mouse = mp:GetMouse()

mouse.KeyDown:connect(function(key)
	if key == "q" then
		mpc.Torso.Anchored = true
		for i=1,5 do
			mpc.Torso.CFrame = mpc.Torso.CFrame * CFrame.new(0,i*2,i)
			if i<5 then
				mpc.Torso.CFrame = mpc.Torso.CFrame * CFrame.Angles(-(i-1),0,0)
			end
			wait(0.25)
		end
		mpc.Torso.Anchored = false
	elseif key == "e" then
		mpc.Torso.Anchored = true
		for i=1,5 do
			mpc.Torso.CFrame = mpc.Torso.CFrame * CFrame.new(0,i*2,-i)
			if i<5 then
				mpc.Torso.CFrame = mpc.Torso.CFrame * CFrame.Angles((i-1),0,0)
			end
			wait(0.25)
		end
		mpc.Torso.Anchored = false
	end
end)

There IS a way to do so, even before ROBLOX made the plugin.

There's a tutorial on the wiki

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Insert an animation plugin for your game. Should work. You have to insert the plugin through studio.