Can a local script access objects from the replicated and server storage?

Like Code1400 said, use a remote event. Keep your LocalScript in your GUI, but insert a regular Script into ServerScriptService. Also insert a RemoteEvent into ReplicatedStorage. Place your object wherever you want because the server can access it anywhere. By the way, make sure your LocalScript is under your ImageButton/TextButton, not the ScreenGui. Now this is what I suggest you have in your scripts:

Local Script

script.Parent.MouseButton1Click:Connect(function()
    game.ReplicatedStorage.RemoteEvent:FireServer()
end)

Script

game.ReplicatedStorage.RemoteEvent.OnServerEvent:Connect(function()
local Money = script.Parent.Parent.Parent.Parent.Parent.Parent.leaderstats["Fish Flakes"].Value
    if Money >= game:GetService("ReplicatedStorage").Skins.DefaultFish.Cost.Value then
            script.Parent.Owned = true  
    end
end)

Hope this helps!

im not sure if they can see anything server sided you have to test that out, but the client can not change any value in the server or they will be kicked from the game. use remote events and functions to do what you want