Without getting to far into it, a a double is presumably when the gene/allele is on both sides of the chromosome (Ie, two copies of the gene). Doubles are hypothetical because of lethality involved, but I will include them here anyway as their is evidence that they may exist and not just be another expression of a single gene. A 'normal red' (Some breeders call them dilute reds, but we will use the term single factors here as it is more correct and more widely used.) has only one copy of the red gene (the other copy is normal), and a normal sun, no red factor genes (two normal copies).
This is a pair of single factors (aka dilute reds or normal reds) which means they have ONE red factor gene, and one normal gene each. Therefore, assuming a simple punnet square, they could theoretically throw (produce in their offspring) NORMAL suns, SINGLE factors, like themselves with one copy of the red gene and one normal gene, and DOUBLE reds (believed to be lethal and connected with metabolic disease), with two copies (25% chance, or one in four, of this happening). Double reds are supposed to be nearly identical, but show more red colouration down the back then singles do.
HYPOTHETICALLY- If the bird is a DOUBLE. Because double reds have two copies of the gene they are desired for breeding, as when mated with a normal sun (100% normal colouration) they will produce 100% SINGLE red factors. When bred to a single red factor they will produce 50% DOUBLE and 50% single. When bred to another DOUBLE they produce 100% double. This is all assuming a standard punnet square method of heredity, but it seems to prove true.
Hypothetical crossings if double itself is not lethal but an extremely close gene locus that always almost inevitability is paired with it is the cause.
Double x Double
x D D
D DD DD
D DD DD
Double x Single
x D D
D DD DD
d Dd Dd
Double x Normal sun
x D D
d Dd Dd
d Dd Dd
Where D is the dominant RED FACTOR allele and d the normal, recessive allele
If he is a SINGLE factor, when bred to a NORMAL (100% normal) sun, the offspring would be 75% NORMAL and 25% SINGLE factor. When bred to another SINGLE, the offspring would be... a 25% chance of a DOUBLE (Potentially lethal) being born 25% of a NORMAL and 50% of a SINGLE factor. When bred to a hypothetical DOUBLE, the offspring would be 50% SINGLE and 50% DOUBLE. Once again, assuming a punnet relation, but it is seen in breedings to be true.
Single x normal sun
x D d
d Dd dd
d dd dd
Single x Single
x D d
D DD Dd
d Dd dd
Single x Double (Hypothetical)
x D d
D DD Dd
D DD Dd
This is all just off the top of my head, so I would run the punnet squares to confirm it beforehand. I use them often in aquaria (Especially in fighting fish matings! Very useful) so I would recommend learning them. I'm curious though, why are you asking, do you intend to breed them?
Edit, fixed an error an threw in the punnets. I assume red factor is dominant.
Edit again- For those that may be confused. D is a single copy of the dominate red allele. d is its normal counterpart. The birds have two genes that control this mutation at a certain location of their chromosomes (one on each side of the pair), and they can be any mix of the two. Therefore DD (D on one side D on the other) is a double factor, Dd (D on one side, d on the other) a single, and dd (d on both sides) a normally coloured sun conure. D is assumed to be dominant based on the documented offspring of various red factor crosses. No sex linkage is assumed (Ie, that red genes are passed on by a certain gender to the offspring)