The Surrealists came out of Dada, and the late Surrealists associated with Andre Breton were explicitly anarchists.
"It was in the black mirror of anarchism that surrealism first recognised itself."
- Andre Breton, 1952 (La Claire Tour)
I have only a passing familiarity with them through listening to a podcast talking about them, but here are some pieces exploring the Surrealists' links with Anarchism:
The 1952 essay La Claire Tour by Andre Breton, also called The Lighthouse or The Tower Of Light.
As to what anarchists might learn from the Surrealists, I have two stories involving Salvador Dali.
In the first, Dali listens to an argument between fellow Surrealists about the the particulars of bombing the first class cars on the train, to which Dali interjected, "The truly revolutionary act would be putting the bomb in a passenger car."
The second is the infamous "Night of Many Sweaters," which you can read more on here:
The thing I take away from both is to always start by attacking the root of things and digging out their very foundations, including those of your own ideas.
Edit: Also, the Night Of Many Sweaters is something I'd like to see more of, just generally. Both in terms of more comedy among anarchists in general, and more engaging with our disagreements as anarchists so directly and fully that we beat our cousins at their own games, aiming to understand them even more fully than do they rather than the dismissal or denunciation that seems the generalized mode among anarchists of late.