DNA is a bit more complicated than some molecules due to it's length and composition variability.
According to Integrated DNA technologies:
DNA oligos can be resuspended to a near maximum concentration of 10mMolar; to achieve such a high concentration will require a lot of vortexing and it may take up to a day for the oligo to go into the solution.
DNA is a polar molecule and as far as I have experienced dissolves in water very readily. However there doesn't seem to be an exact quantifiable number for DNA solubility in water. If I correctly understand it, this paper claims that a 200,000Da-8,000,000Da oligonucleotide is soluble in water, however they never quantify this. An answer on a related question pointed out that high molecular weight DNA oligomers, like genomic DNA, is enhanced in solutions with dilute monovalent cations.
Cleaver & Boyer (1971) have some data on this, however it is somewhat outdated, and they were only using this solubility to demonstrate dialysis in water was capable of desalting the oligonucleotides.
Oligonucleotides larger than 5 bases in length remained within the dialysis
bag (Fig. 2) and losses of 10% and 40% occurred for tetra- and trinucleotides,
There is a lot of work done on optimal temperature and pH for solubility of DNA so perhaps a more specific query might throw up some results.
Ethanol precipitates at least 10–20 % of all classes of oligonucleotides. Oligonucleotides longer than 15–16 nucleotides are precipitated to about 65%.