First, let's look at a flowchart explaining how Chains of Mephistopheles works.
Now, when you go to draw a card (other than the one that is a turn based action during your draw step) you have 2 replacement effects trying to replace that draw, the Chains and Dredge. You get to choose which one to apply first (616.1).
- If you choose to apply Dredge first you can no longer apply the Chains since you are no longer drawing a card (614.6).
- If you choose to apply the Chains effect first you can still Dredge as long as you would draw a card after discarding, if you mill (because you had no cards to discard) you cannot apply Dredge.
616.1. If two or more replacement and/or prevention effects are attempting to modify the way an event affects an object or player, the affected object’s controller (or its owner if it has no controller) or the affected player chooses one to apply, following the steps listed below. If two or more players have to make these choices at the same time, choices are made in APNAP order.
614.6. If an event is replaced, it never happens. A modified event occurs instead, which may in turn trigger abilities. Note that the modified event may contain instructions that can’t be carried out, in which case the impossible instruction is simply ignored.
You choose which ones apply. If you use the Dredge effect, the Chains effect doesn't apply any more, so you'll just mill two cards and put the Dakmor Salvage into your hand. If you have at least one card in your hand, you can also choose to apply the Chains effect, then the Dredge effect, so you'd discard a card, then mill two cards and put the Dakmor Salvage into your hand. And if you don't have a card in your hand, then you can choose to just mill one card.
Both of those are replacement effects that modify a card draw. Chains of Mephistopheles' effect is complicated, but there's a ruling that explains it as simply as possible:
Here's what happens when Chains of Mephistopheles replaces a player's draw:
- If that player has at least one card in his or her hand, he or she discards a card and then draws a card.
- If that player's hand is empty, he or she puts the top card of his or her library into his or her graveyard. The player doesn't draw a card at all.
And Dredge's effect is fairly simple, as described in rule 702.51a:
Dredge is a static ability that functions only while the card with dredge is in a player’s graveyard. “Dredge N” means “As long as you have at least N cards in your library, if you would draw a card, you may instead put N cards from the top of your library into your graveyard and return this card from your graveyard to your hand.”
They are both replacement effects, so their interaction is governed by the interaction of replacement and/or prevention effects rules. Basically, the player affected applies applicable replacement effects at most once each until no more of them are applicable, then follows the resulting instructions.
So, you can choose to apply the Dredge replacement first. In that case, you are no longer drawing a card, so the Chains replacement doesn't apply any more.
You can also choose to apply the Chains replacement first. In that case, what you do depends on whether your hand is empty. If it is, then you are again no longer drawing a card, so the Dredge replacement doesn't apply any more. If your hand is not empty, then you are still drawing a card, so the Dredge effect still applies and you can apply it too.
You can choose the dredge replacement effect instead of Mephistopheles. What you also can do is when let the replacement make you discard the second card you draw for the turn and then draw a card.
Seeing as the Oracle text for Chains of Mephistopheles specifically mentions...
If a player would draw a card except the first one he or she draws in his or her draw step each turn, that player discards a card instead. If the player discards a card this way, he or she draws a card.
You will now have the chance to discard the card you draw and then also dredge. Seeing as this is a dredge deck and you want to dump as many cards into the graveyard as possible this may be better.