How to get “Final Countdown” Spell card in Duel Links?
At the time of this answer's writing,

Final Countdown is not obtainable in Duel Links.

To verify this, you can search for it within the View/Convert Cards section of the Deck Studio. Doing a text search for the word "final" shows six cards - none of which are Final Countdown.

Moreover, according to the Yu-Gi-Oh! wiki, neither  does a skill which adds Final Countdown to a player's hand or deck currently exist.