Obviously DNA is a very fragile construction. The most obvious manifestation of this is a very well-known and prevalent disease known as cancer.
We would need multiple redundant copies of the stored DNA information in the test subject to avoid information loss, as we have with our functional DNA. These copies ideally would be spread throughout a variety of different cells, making it probably the best to insert several modified cells containing our genetically encoded information in a developing human embryo to let it multiply later. (Obviously, ethical issues would abound here.)
Our next question is where this data would be encoded. Obviously, for us to have a functional human, our data can't overwrite existing DNA. One place someone could insert information would be in the telomeres of chromosomes, which are long strips of redundant genetic information that are slowly stripped away as a cell replicates over and over again. Obviously, as the person ages, more and more information would be lost due to the telomeres' length shortening, making this an undesirable solution in the long term. However, to store data in the short term, this could potentially work.
As for parenting, there could be some issues with data retrieval. Meiosis is a complicated process that involves some genetic switcheroos between various chromosomes in a process known as crossing over, and data could be mixed up or split apart in that process. (After all, the whole point of reproduction is to induce genetic variety in offspring, not to prevent genes from changing.) So I wouldn't bet on all of the information surviving.