A favor is around 1-5 energy per turn, depending on how the particular AI you have favors with feels about you. So, the question you posed is not an easy one because favors themselves don't have a constant value, but are themselves affected (value-wise) by your standing with the target AI.
That being said, I've never actually tried to use favors alone to get a DoW on one AI from another. I'd imagine it might be not many favors at all in some cases (if the AI is already wanting to attack) or could be flat-out impossible no matter how many favors you have (i.e. the AI is on better terms with the target than with you).
Favors are mostly worth while only when you have something you don't need (like an affinity-aligned resource) prior to the AI having anything worth trading for it. Favors are basically an I.O.U. for later on when the AI will finally have connected a resource you would like to trade for or will have enough energy to trade.
Bear in mind that favors are cancelled out with someone if you go to war with them, regardless of who DoWed who. So storing up favors itself is riskier than simply trading a resource for energy, or vice-versa. However, this cuts both ways, and you can cancel out another side's favors with you by attacking them.
