Nicely drawn Columbia ad for this record uploaded, showing that "That Will Be Alright" was actually the A-side. As Columbia ads were published in each issue of this weekly paper and this record was first advertised in the August 3, 1929 (Saturday) issue, it was most probably released on Friday, August 2, 1929.
[Edit: confirmed by Dan Mahony, The Columbia: 13/14000-D Series, page 49]
"When The Levee Breaks", recorded only two years after the Great Mississippi Flood of 1927, was later covered by Led Zeppelin. This here is a rather calm and modest recording compared to the mighty Led Zep cover, smoothly sung by "Kansas" Joe McCoy (whose voice I actually prefer to Minnie's) with elaborate guitar accompaniment by his then partner and wife.