I don't know of a very direct connection, but I'll suggest a circuitous one:
If the methylation cycle is partially blocked, this also disrupts the folate metabolism, because the two are linked together by the methionine synthase reaction. This causes draining of folates from the cells into the blood by the so-called "methyl trap" mechanism. With low folates in the cells, they are less able to make new DNA, which is necessary for them to divide to make new cells. This problem shows up most strongly in the cell types that normally reproduce fairly rapidly, because they have short lifetimes. This includes some of the blood cell types, as well as the cells lining the intestine. If new cells are not made rapidly enough in the intestine to replace the older ones that are being sloughed off, I think this could contribute to developing a leaky gut. A leaky gut will allow oxalates, which come in with food, to enter the blood. They are filtered out of the blood by the kidneys. If oxalate encounters calcium under appropriate conditions, it will react to form the highly insoluble compound calcium oxalate. This can contribute to the formation of kidney stones. Does this scenario really happen? I don't know, but I think it is a plausible hypothesis.