Random Jump animation is not working?

You can simply use math.random().

while wait() do 
    local random = math.random(1, 2)
    if random == 1 then
        animateScript.jump.JumpAnim.AnimationId = "rbxassetid://5620182994"
    else
        animateScript.jump.JumpAnim.AnimationId = "rbxassetid://5620201065"
    end
end

Lemme know if it works!

You can check for player state when the player jumps. If the new state is Enum.HumanoidStateType.Jumping, they're jumping! This means you can reselect another animation randomly each time they jumps.

Use LocalScript for this.

local plr = game.Players.LocalPlayer
local char = plr.Character or plr.CharacterAdded:Wait() --Waits for their character to get their humanoid

local hum = char:WaitForChild('Humanoid') --again, wait for their humanoid if it's not loaded yet

local anims = {
    "rbxassetid://5620182994",
    "rbxassetid://5620201065"
}

local animObj = animateScript.jump.JumpAnim --Your animation object here.

local changeAnimation = {
    [Enum.HumanoidStateType.Jumping] = true
    --You can add more states here if you want multiple states to run animation rotation.
    --If you don't want any more states, use Humanoid.Jump event instead.
}

--Humanoid.StateChanged -> (oldState, newState)
--no need oldState for this
hum.StateChanged:Connect(function(_, newState)
    --Use dictionary indexing to find if this is the state you want the animation to be updated the next time you jump.
    if changeAnimation[newState] then
        --Use math.random!
        animObj.AnimationId = anims[math.random(1, #anims)] --This gets one animation id and update the AnimationId property.
    end
end)

Just to make sure, you should use humanoid:LoadAnimation(animationObject) in case you want to play this animation yourself when the player jumps.