I sought to research the storyline of Icarus to gather a more original form of the myth. I spoke to lecturer of Ancient of Greek at the University of Exeter who emailed me a resource for pretty much anything Ancient Greek.
“The well-known version of the story is formulated in Ov. Met. 8,183-235 (cf. Apollod. Epitome 1,12f.); a Pompeiian fresco is from about the same time. It is difficult to make out what earlier tales were like: first, but recognizable only in outline, is the myth in Attic tragedy (since Aesch. Pers. 890; the lost ‘Cretans’ of Euripides were important), and whether the version, recorded since the 4th cent., that the Icarian Sea takes its name from I. falling from his father's ship and drowning (Menecrates of Xanthus, FGrH 769 F 1) precedes the tale of the flight or rather rationalizes it (cf. Diod. Sic. 4,77,6; Paus. 9,11,2), is unclear; the oldest pictorial representation (an Attic black-figured skyphos from about 600) shows only Daedalus. Despite the aetiology which clearly points to the island Icarus/Icaria and the Icarian Sea, I. probably first belonged in the Attic Icaria ( Icarius), which neighboured the deme Daedalidae; Daedalus himself is an Athenian, son of Metion (Pherecydes FGrH 3 F 146)…..The main source of the story is Ovid’s Metamorphoses book 8.”
Source: http://www.perseus.tufts.edu/
Ovid’s Metamorphoses Book 8
Ive highlighted the key points in this version of Icarus for anything I feel could be relevant when transcribing this version
DAEDALUS AND ICARUS
But Daedalus abhorred the Isle of Crete—
and his long exile on that sea-girt shore,
increased the love of his own native place.
“Though Minos blocks escape by sea and land.”
He said, “The unconfined skies remain
though Minos may be lord of all the world
his sceptre is not regnant of the air,
and by that untried way is our escape.”
This said, he turned his mind to arts unknown
and nature unrevealed. He fashioned quills
and feathers in due order — deftly formed
from small to large, as any rustic pipe
prom straws unequal slants. He bound with thread
the middle feathers, and the lower fixed
with pliant wax; till so, in gentle curves
arranged, he bent them to the shape of birds.
While he was working, his son Icarus,
with smiling countenance and unaware
of danger to himself, perchance would chase
the feathers, ruffled by the shifting breeze,
or soften with his thumb the yellow wax,
and by his playfulness retard the work
his anxious father planned.
But when at last
the father finished it, he poised himself,
and lightly floating in the winnowed air
waved his great feathered wings with bird-like ease.
And, likewise he had fashioned for his son
such wings; before they ventured in the air
he said, “My son, I caution you to keep
the middle way, for if your pinions dip
too low the waters may impede your flight;
and if they soar too high the sun may scorch them.
Fly midway. Gaze not at the boundless sky,
far Ursa Major and Bootes next.
Nor on Orion with his flashing brand,
but follow my safe guidance.”
As he spoke
he fitted on his son the plumed wings
with trembling hands, while down his withered cheeks
the tears were falling. Then he gave his son
a last kiss, and upon his gliding wings
assumed a careful lead solicitous.
As when the bird leads forth her tender young,
from high-swung nest to try the yielding air;
so he prevailed on willing Icarus;
encouraged and instructed him in a]l
the fatal art; and as he waved his wings
looked backward on his son.
Beneath their flight,
the fisherman while casting his long rod,
or the tired shepherd leaning on his crook,
or the rough plowman as he raised his eyes,
astonished might observe them on the wing,
and worship them as Gods.
Upon the left
they passed by Samos, Juno's sacred isle;
Delos and Paros too, were left behind;
and on the right Lebinthus and Calymne,
fruitful in honey. Proud of his success,
the foolish Icarus forsook his guide,
and, bold in vanity, began to soar,
rising upon his wings to touch the skies;
but as he neared the scorching sun, its heat
softened the fragrant wax that held his plumes;
and heat increasing melted the soft wax—
he waved his naked arms instead of wings,
with no more feathers to sustain his flight.
And as he called upon his father's name
his voice was smothered in the dark blue sea,
now called Icarian from the dead boy's name.
The unlucky father, not a father, called,
“Where are you, Icarus?” and “Where are you?
In what place shall I seek you, Icarus?”
He called again; and then he saw the wings
of his dear Icarus, floating on the waves;
and he began to rail and curse his art.
He found the body on an island shore,
now called Icaria, and at once prepared
to bury the unfortunate remains;
but while he labored a pert partridge near,
observed him from the covert of an oak,
and whistled his unnatural delight.
Know you the cause? 'Twas then a single bird,
the first one of its kind. 'Twas never seen
before the sister of Daedalus had brought
him Perdix, her dear son, to be his pupil.
And as the years went by the gifted youth
began to rival his instructor's art.
He took the jagged backbone of a fish,
and with it as a model made a saw,
with sharp teeth fashioned from a strip of iron.
And he was first to make two arms of iron,
smooth hinged upon the center, so that one
would make a pivot while the other, turned,
described a circle. Wherefore Daedalus
enraged and envious, sought to slay the youth
and cast him headlong from Minerva's fane,—
then spread the rumor of an accident.
But Pallas, goddess of ingenious men,
saving the pupil changed him to a bird,
and in the middle of the air he flew
on feathered wings; and so his active mind—
and vigor of his genius were absorbed
into his wings and feet; although the name
of Perdix was retained.
The Partridge hides
in shaded places by the leafy trees
its nested eggs among the bush's twigs;
nor does it seek to rise in lofty flight,
for it is mindful of its former fall.”
This source have given me a good idea to what the original myth might be and putting. There are many parts of the story I will mention because they doesn't seem relevant and because of course this a is children's book. But there are parts than can be seen in the artwork that gives this book some authenticity.
Gerald Scarfe is a British Illustrator and cartoonist he is most famous for his work on pink Floyds wall. The work of his that I feel is great reference and influence is the production design he done on Disney's Hercules. I found the book “The Art of Hercules” which contains much of his work on the film along with others 
