Alliteration is very common throughout Gerard Manley Hopkins's poetry, and "Felix Randal" is no exception. Generally speaking, this poem uses alliteration to intensify its images—to make them more vivid and lively on the page and to the ear.
The first example of alliteration is in the poem's opening line: "Felix Randal the farrier." This type of description uses what is known as an epithet, in which a person's name is linked to something defining about them, like their occupation or a particular trait (e.g., Alfred the Great). In this case, the alliteration makes the bond between name—Felix—and job—farrier—extra strong, as though in tribute to the nature of this work itself. That is, a farrier (someone who makes and fits horseshoes), has to create strong, dependable objects—reliable joins between different pieces of metal and, of course, between the horseshoe and the horse's hooves. The strong sonic link between "Felix" and "farrier," then, not only links the dead man to a picture of him as a strong worker but also relates to the kind of quality work he had to produce.
Three examples of alliteration in line 2 also support this idea of Felix Randal as a strong, vigorous young man. The speaker wants the reader to get an idea not just of the tragedy of Felix Randal's death, but of the way he was once so physically impressive, so vibrantly alive. "Mould of man, big-boned and hardy-handsome" ring out bold and clear, representing Felix Randal's once-impressive physicality.
Later in the stanza, alliteration is associated with Felix Randal's deteriorating condition, implying that a new kind of strength—the disease's—started to win out over Felix's own: "reason rambled [...] Fatal four disorder, fleshed there."
In the second stanza, the speaker describes how, in his role as priest, he was able to help Felix come to terms with his imminent death. The light, lovely sound of "heavenlier heart," which is what Felix developed through conversation and contact with the speaker, indicates a turn towards sacred and spiritual comfort. The gentle sibilance of "some," "since," and "sweet" in lines 6-7 give the reader a sense of the tenderness with which the speaker treated Felix Randal.
Interestingly, though, the /s/ carries different connotations in line 9 (working with the internal consonance found in the line). Here, there is almost too much of the /s/ sound, conveying a kind of sickliness, with the poem's voice reducing to a sibilant whisper to suggest the physical difficulty Felix Randal faced in his dying days:
This seeing the sick endears them to us, us too it endears.
The rest of the stanza features prominent /t/ alliteration that contributes to an atmosphere of tenderness that is not without its suggestion of physical pain:
My tongue had taught thee comfort, touch had quenched thy tears,
Thy tears that touched [...]
Finally, alliteration works in harmony with assonance and consonance in the poem's closing lines to create a vivid image of Felix Randal in his prime—hard at work in his blacksmith's workshop, making and fitting horses shoes for a "great grey drayhorse":
How far from then forethought of, all thy more boisterous years,
When thou at the random grim forge, powerful amidst peers,
Didst fettle for the great grey drayhorse his bright and battering sandal!
The sounds here conjure the atmosphere of the workshop, which, of course, would have been full of loud noises. But, as mentioned at the start of this analysis, the sounds also work to intensify what's being described. That is, alliteration makes Felix seems more "powerful amidst [his] peers," the horse more "great [and] grey,"—and the "bright and battering" sandal more perfect.