There is no way to unlock Suicune until you have caught 60 Pokemon in your Pokedex. Then, the only way to find him is to wander in the wild until he appears. Every time you switch routes, so does he. Use this to your advantage, if you're not finding Suicune, change routes and so will he!
Keep in mind Suicune is only unlockable if you picked Charmander as your stater.
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A faster way to get an egg to hatch is to ride your bike.
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Flame body but this only works in Pokemon emerald, pearl, diamond, platinum, heartgold, soulsilver, black, white so far (ruby, sapphire, firered, leafgreen do not have the out of battle effects with abilities)
There is no Pokemon moon game.
Train them............