Learn French: Nous devons planter plus d'arbres indigènes.

Yes, you could absolutely say Nous devons planter davantage d'arbres indigènes. Both mean the same thing, but davantage is slightly more formal or literary. Remember that while plus is versatile, davantage is only used for quantities of things or actions, making it a perfect fit here.

Why is it d'arbres rather than des arbres, since the trees are plural?

Because plus acts as an adverb of quantity here. Just like with beaucoup de or moins de, the rule is to use the bare preposition de (which becomes d' before a vowel), regardless of whether the following noun is plural.

Is the 's' at the end of plus pronounced in this sentence?

No, it is silent. When plus is followed by de or d' to express a quantity, the 's' is not pronounced. You generally only hear the 's' when plus means "more" at the absolute end of a phrase, or when making a liaison before a vowel.

Could I use natifs instead of indigènes for "native" trees?