I’m reading The Ballad of the White Horse by G.K. Chesterton, which is an epic poem that follows King Alfred the Great and his battles against the Great Heathen Army. I was wondering if there is any poetry from the Norse people about the same events.
Put it simply, no.
The most conspicuous reason is: AFAIK No known Scandinavian (especially Norwegian) ruler had been present at the battle so that no historical writing on the battles in the Britain in the late 9th century was written in medieval Iceland later, so all the possible Norse poems composed for commemorating the battle would have soon been forgotten in oblivion in course of time. Even almost all of the extant 'historical' skaldic poems allegedly composed in the 9th century and dedicated to the Norwegian ruler has been doubted their authenticity by many scholars.
It is also worth noting that the majority of the extant Old Norse-Icelandic poems were in fact allegedly composed by the Icelandic poets rather than some Norwegian ones. There have probably been more 'forgotten' poets, especially Scandinavian ones, whose work was not cited in later literature, as suggested by the very uneven distribution of Icelandic skaldic poets, divided by individual Scandinavian rulers, composing all the three Nordic kingdoms in Skáldatal (Catalogue of the poets). In short, it is likely that the contemporary court had also been open to non-Icelandic Scandinavian poets, but their works were just not cited in medieval Icelandic parchments, so they were lost in course of Middle Ages or even earlier.
The closest extant literary work (poem) OP is looking for is probably the poem Darraðarljóð in which valkyries are weaving the destiny of coming battle [traditionally identified with the battle of Clontarf in 1014], only extant in form of citation in famous Njal's saga (linked to the dated translation to the saga, together with the poem). While I'm rather doubtful about the poem's authenticity, the poem itself seems to have certainly been older than the prose part of the saga (so some scholars even suggest that the extant poem had not originally been composed about the battle of Clontarf, but another battles during the Viking Age.
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