Evidence against aging caused by loss of information in genome and epigenome in humans?

From what I know, I would expect that no one has performed a similar experiment to what you propose. Sequencing a genome is still rather expensive and inaccurate. Some parts of the DNA can’t be sequenced at all and most methods still rely on comparing the sequencing reads to a reference genome, making these kinds of predictions harder. Getting snapshots of an epigenome (chromatine modifications, transcription factors) to the accuracy that you can detect a notable difference after a few years is even harder.

Also, by analyzing the genome of a given somatic cell, the cell is being destroyed and not available to test it again after a couple of years to see if relevant mutations occurred.

In short: Sinclair‘s predictions are probably hard to verify at this point.

By loss of genome, I think he is referring to the shortening of telomeres. This study compares the length of telomeres of human epidermal cells. The authors report that over time, the telomeres do shorten. They also report on the rate of loss of around 32 base pairs per year. Thus there is loss of some genomic information over the age of an individual.

However, the loss of epigenomic information is trickier. The primary reason for it being some regions of the genome have been shown to lose DNA methylation marks whereas others gain it. However, leaving that aside, there is comprehensive proof that DNA methylation changes with age. This study on female peripheral leukocytes shows that approximately 350 regions (known as CpG islands) which are differentially methylated with age. Of these 350, 250 loci become hypermethylated i.e. methylation increases with age while the opposite happens for the remaining 150 loci.