To my (American) ear, the phrase "a gentleman of property" sounds like quaint British English. I might expect to find this phrase in a Jane Austen novel (written in the early nineteenth century) or perhaps in a Charles Dickens novel (written in the mid-nineteenth century).
Within that context, it is idiomatic for "an upper-class man who owns enough income-producing property that he does not need to work for a living."
This particular quotation is from a [wikipedia article][1]Wikipedia article about a seventeenth-century soldier/physician. The article was [originally copied][2]originally copied from a 1911 Encyclopædia Britannica [article][3]article, which had a longer description: "a gentleman of property and good pedigree."
[1]: http://(https://en.wikipedia.org/w/index.php?title=Thomas_Sydenham&oldid=733514932 [2]: https://en.wikipedia.org/w/index.php?title=Thomas_Sydenham&oldid=4103414 [3]: https://books.google.com/books?id=ITsbAQAAMAAJ&pg=RA1-PA277&lpg=RA1-PA277#v=onepage