There are probably many questions regarding whether or not Kratom will show up on a Drug test. Keep in mind that when a company issues a drug screening for a new hire they are often looking for specific drugs. This will, of course, vary company to company. I can speak on this first hand and have seen documentation and spoken to human resources representative from a well known hospital in Southern California regarding their testing protocols.
I'm sure you've heard the story of someone eating a poppy seed bagel and then taking a drug test where the results showed trace amounts of opium. In this case, poppy seeds do show a false positive. This is not the case with Kratom. Although Kratom does affect the brain receptors similarly to an opiate, it does not register as an opiate on a drug test. With that said, if a company decided to list Kratom as a drug of concern and specifically test for components of Kratom, such as the alkaloids mitragynine and speciogynine, they would show in the urine as markers. Because Kratom is legal and to my knowledge not tested for, you should have nothing to worry about.
To take it even further, although a urine test is common there are more specific drug tests such as an Immunoassay test done by Gas chromatography–mass spectrometry (GC/MS) quantitative test. An example of Immunoassay is Enzyme-linked immunosorbent assay (ELISA) and when conducted, antibodies are created which bind to specific chemicals such as THC when looking for Marijuana. These tests will detect the presence of a chemical and not necessarily the amount. Semi-quantitative immunoassays will give an approximation of the amount. These tests can be used to detect Cannabinoids, Cocaine, Amphetamines, PCP, LSD, Opioids, Barbiturates, Ethanol, Benzodiazepines, Ketamine and so on. With these tests there would be no false positives. In addition, quantitative confirmation tests are chemically specific and there are none for Kratom.
More advanced tests become cheaper every day, but as long as Kratom is legal I wouldn't spend too much time worrying about it.