LaVon, to estimate a yDNA haplogroup from your AncestryDNA autosomal results you may find a free utility called Cladefinder (https://cladefinder.yseq.net/) to be easier and more current. Written by WikiTree members Hunter Provyn and Thomas Krahn, it uses a real-time connector to the haplotree at YFull rather than relying on a static, older database. You can read more about it in a G2G thread from last April. Be aware, though, that the haplogroup returned is likely to be many hundreds if not thousands of years old. It can be used to tell if two men are not related, but it requires deeper, for-purpose testing to use yDNA as positive evidence that they are related.
If the Johannes Vineyard born 1716 is the ancestor of interest, Peter is correct that yDNA will be the better avenue for genetic comparisons than autosomal DNA, like your Ancestry test. If a test-taker was born in 1960, Johannes would be (using a typical generational interval) about 9 generations back, or a 7th great-grandparent. At that distance, contemporary test-takers today would be 8th cousins to each other, or some flavor of 7th cousin X-times removed (with each "removal," the expected amount of DNA sharing is halved). By the time you get to 7th cousins, the chances that two people share any detectable DNA from the same ancestor is about 0.6%; for 6th cousins that number is 2.1%. (A small chart I prepared a few years ago.) And even if detected, it's extraordinarily difficult--and often not possible--to validate the genetic inheritance path that far back.
Autosomal DNA recombines in the parent so the child gets 50% of each parent's DNA, and each sibling gets a different 50%. That it makes autosomal DNA extremely valuable in genealogy for several generations in the past, but it quickly reaches a point of diminishing returns. Unlike autosomal DNA, the Y chromosome doesn't go through recombination and is passed down largely intact from father to son, so it allows us to use small, infrequent mutations to look much, much farther back in time.
