Use DistributionFitTest. Here is an example I ran with some random data (certainly does not fit the Burr distribution).
data = RandomReal[{0, 1}, 400];
test = DistributionFitTest[data, SinghMaddalaDistribution[2, 2.5, 3],"HypothesisTestData"];
test["TestDataTable", All]
The Burr distribution is called the Singh-Maddala distribution in Mathematica (and in many other places). The output of the last command will be a table with the results (statistics and p-values) of applying the tests Mathematica considers appropriate for the data used (Anderson-Darling, Cramer-von Mises, Kolmogorov-Smirnov, etc.).
Notice that one needs to enter the distribution parameters one wants to test. That is generally necessary, except for distributions that are 'nicely' scalable, such as the normal distribution. If you think some distribution of this type should fit your data, but you are not sure what parameters would work, then you are dealing with a different problem and you should use a different tool (in that case I would use FindDistributionParameters).
Best,
OL.