Scrap comes from cards, so "Best" is a bit fuzzy. You’ll need to add cards to your deck.
All lodging cards have an option that grants Scrap. Fancier lodgings grant more scrap. The four-card lodgings are the best (especially Bazaar Premises), but they all add up.
Calling in Urchin Favors in the Flit gives 25 scrap. If you are seriously devoted to grinding scrap, the Flit is where you will draw all your cards and that is what you will use it for. Also, get items that add cards that grant Urchin favors (Connected Pet & Winsome Dispossessed Urchin at minimum).
I hear there’s one Fate story where one ending adds a Scrap rewards to one Faction card?
So about gambling with the Relickers… theoretically, if you use the Armful or Double Armful options, you will on average gain 1 scrap per action. This isn’t very good, but it’s also high-variance. You will have to decide for yourself whether your own personal relationship with the RNG would make this a good idea or not. (Personally I gamble almost always, and am now up 540 scrap on ~600 draws.)