There is a reasonable (to me) stab at an explanation here
http://bob-dylan.org.uk/archives/1746#comment-311867 

Sam the Sham says:

This might be my favourite Dylan song and I think I owe it to everyone to explain what the song means.

"Farewell Angelina – Essentially the beginning of a goodbye love letter from the dead.
The bells of the crown – The bells are a metaphor for a reason to start a war but bells are also musical which ties into the next sentence.
Are being stolen by bandits – Again the reason for war. The bandits are the other side who started the war.
I must follow the sound – The sound is of a funeral march
The triangle tingles – A musical reference to a funeral march
And the trumpet play slow – A musical reference to a funeral march
Farewell Angelina –
The sky is on fire – The war is starting
And I must go

There's no need for anger -Let's enjoy our final time together
There's no need for blame – The decision wasn't up to me. Let's not fight during my last moments with you
There's nothing to prove – We know we love each other. We don't need to say it
Everything's still the same – At this point in time, nothing has chanced
Just a table standing empty – However our future metaphorical table is empty. Because he will be dying.
By the edge of the sea – The sea represents time as well as the fact the war is over in Europe where he takes a ship
Farewell Angelina –
The sky is trembling – The personification of his feeling onto the sky
And I must leave – But this is his duty

The jacks and queens -metaphor for politicians
Have forsaken the courtyard – the are making the decisions. Forsake is a negative word
Fifty-two gypsies Now file past the guards – cards are a metaphor for gambling. We can assume the soldiers are the gypsies practicing in front of the gards
In the space where the deuce And the ace once ran wild. He is saying in the past the card game of choice was Ace and Deuce Wild. What he is saying is gambling has always taken place here.
Farewell Angelina –
The sky is folding – Again personification of the sky with a another card metaphor when he uses the word folding. Folding is the disbelief that the sky is in or god for the horror.
I'll see you in a while – This is likely in reference to that he will see her in heaven.

See the cross-eyed pirates sitting – Dylan is establishing that people at home are pirates a negative connotation
Perched in the sun – To them the war is bliss
Shooting tin cans – Essentially they are enjoying war. We saw people excited in WWI for the prospect of war
With a sawed-off shotgun – A sawed off shot gun would show their low class.
And the neighbors they clap – Again excitement for war
And they cheer with each blast – People at home love war
Farewell Angelina
The sky's changing color – A new somber mood
And I must leave fast – He just left

King Kong, little elves – We all have an image in our head how king kong is being attacked by planes etc on a building.
On the rooftops they dance – King Kong is on a rooftop they are all dancing a euphimism for fighting
Valentino-type tangos – This is another dance metaphor for fighting.
While the make-up man's hands -hand to hand combat
Shut the eyes of the dead – One of Dylan's best lyrics ever. What Dylan is saying here is that people are dying in war but he feels bad for the dead. He wants to shut their eyes so they are not embarrassed to have died for such a useless purpose.
Not to embarrass anyone – The dead would be embarrassed if they saw this.
Farewell Angelina –
The sky is embarrassed – God and everyone is embarrassed
And I must be gone – He is already there so this means he knows he will die.

The camouflaged parrot, he flutters from fear -camouflage is a metaphor for someone in the army. Typically people in the army wear camouflage gear.
A parrot repeats what is told of them. Therefore army soldiers are camouflaged parrots according to Dylan.
When something he doesn't know about suddenly appears – The parrot is the guy singing the song. Someone appears out of nowhere. AKA some enemy soldiers appears
What cannot be imitated perfect must die – His training wasn't perfect and he will die here
Farewell Angelina, the sky is flooding over and I must go where it is dry – Could be a reference to blood and getting out of the battle. Basically his corporal will take him out and he is in the hospital. Or sky flooding over could be the fact the sky is getting darker and he is getting closer to death.

The machine guns are roaring – battle continues
The puppets heave rocks – Before they were parrots who repeat now the soldiers are puppets controlled by higher powers. Rocks can be grenades or bombs.
The fiends nail time bombs – A time bomb would be in reference to the length of time to die
To the hands of the clocks -I think Dylan is saying that the soldiers are clocks AKA they have a lifespan. Also I think a clock could be in reference to a tombstone.
Call me any name you like – His lover can say anything to him now
I will never deny it – He can't defend himself because he is dead.
Farewell Angelina –
The sky is erupting – War is terrible
I must go where it's quiet – Rest in Peace