Question

How can I breed to get a Swinub that knows Ancient Power?

Answer 1

You dont breed a swinub to get ancientpower. What you do is evolve it into a piloswine and then go to the move rememberer with a heart scale and piloswine will learn ancientpower. Just level it up once and it will evolve after you make the piloswine remember ancientpower.
Source: http://bulbapedia.bulbagarden.net/wiki/Piloswine

Answer 2

The easiest way I found to breed a swinub with ancient power is to first breed a wooper with ancient power using a shellos or gastrodon.
Here you can see wooper (or quagsire) can learn Ancient power via breeding with shellos (or gastrodon) :
https://pokemondb.net/pokedex/wooper/egg
And here you can see that swinub learn ancient power via breeding with wooper (or Quagsire) :
https://pokemondb.net/pokedex/swinub/egg