I'm finding it really hard to analyse Lorca's poem "La guitarra." I understand the flamenco influence but I'm struggling after that. Any suggestions?

La Guitarra has not much to do with the flamenco influence except in form, not essence. What I mean by this is that he chose the guitar metaphorically to represent the imminence of life and death, love and hatred, joy and happiness, and how the guitar can represent all these things that just do not stop happening throughout one's existence.

The guitar playing as the goblets crash

Se rompen las copas de la madrugada
     It rends the chords of the sunrise
Empieza el llanto de la guitarra
     When the crying of the guitar begins
Es inutil callarla, es imposible callarla.
     It is useless to hush it, it is impossible to hush it up.

In here, the guitar is the feeling of life, the drunkenness of joy, and happiness, but that also can be interpreted differently since the drunkenness can also be brought in by disappointment, and intense pain- Either way does not matter: What matters is that life goes on- just like the guitar keeps playing.

Llora monotona como llora el agua,
     It cries monotonously like the crying of water,
Como llora el viento sobre la nevada.
     The way wind weeps over the snow.
Es imposible callarla,
     It is impossible to silence it,
Llora por cosas, lejanas.
     It cries for distant things.

Here is another allusion to life and our own dreams of having that we cannot have, or trying to reach goals that we may never get. It is another one of those sad realities that, when they hit, they hit hard. And, like the guitar, it may be impossible to avoid. Another allegory is nostalgia and remembrance for, as we age, we lose friends along the way, and we end up basically alone- another sad reality. And, again like the guitar, it is inevitable- it just won't stop its tune.

Arena del sur calliente
     The hot sand of the south
Que pide camelias blancas
     Thirsty for the white camelias
Llora flecha sin blanco
     It decries the arrow shot wide of the target
La tarde sin manana.
     The darkening of the hour without the promise of morning.

This one is easier to debunk because he looks back into his own life and his nostalgic memories of his hometown (sands of the south) and its yearning for peace (white camelias), and hating the destructions caused by war. By this Lorca also means how music is a universal art of peace. The guitar could here represent pure nostalgia, as he remembers his past.

Y el primer pajaro muerto
     And the first dead bird
Sobre la rama. guitarra
     Fallen from the branch.  Oh, guitar,
Corazon malherido por cinco espadas.
     Your heart cruelly wounded by five sharp swords.

Here the five sharp swords are the fingers of the guitar banging at the center of it as the intensity of Lorca's work becomes more, and then-death- the first dead bird meaning the ending of life, and the sound of the guitar represents the beating of our hearts, coming to a stop.

It may not make a lot of sense, but remember that Lorca comes from a literary period in which the sad and the nostalgic were always summoned. His prose is no different,and it is not surprising to sort of see how he is a bit hyperbolic and extreme in trying to touch on the audience's heart. It is part of the movement, and the style of his generation.