If you control Teferi’s emblem, the rule that says you can activate a loyalty ability only if none of that permanent’s loyalty abilities have been activated that turn still applies. In other words, you could activate a planeswalker’s loyalty ability once on your turn and once on each of your opponents’ turns.

If you control The Chain Veil (from the Magic 2015 core set) and its activated ability has resolved, and you also control Teferi’s emblem, for each planeswalker you control, you can activate one of its loyalty abilities during that turn any time you could cast an instant, and then you may activate a loyalty ability again that turn (choosing the same loyalty ability or a different one) any time you could cast an instant.