Here is a link to a variety of unemployment and employment statistics from the Bureau of Labor Statistics.
After selecting the data at which to look (check the boxes to the left in the column of descriptions, then go to the bottom of the list and click on “retrieve data”), plotting the data is easy to do – just click the “include graphs” box and then the blue “go” circle, toward the top of the form. The plots show that the overall unemployment rate and the unemployment rates in the racial/ethnic subclasses have been going down in a mainly linear fashion since January of 2010 or 2011. Most of the fall since the recession was during Obama’s administration.
Trump is correct that the unemployment rate for Blacks or African/Americans is currently 5.9 (June 2018). For once, Trump was not lying.
At the middle of the first year of his administration, July 2017, the rate was 7.1, so in a year we have seen about a one point drop, which agrees with the yearly decreases under both Obama and Trump. Whether the levels are the lowest ever, I do not know, but I do not think Trump does either.
I chose to look at the data from Trump’s administration six months in because, with a new presidency, there is a period of adjustment as policies from the former administration are phased out and the policies of the new administration are put in place.