Just to add to what John answered below, "accredited DNA lab" generally means one used for judicial, forensic, or government identification purposes. These won't do you any good because they test for a couple dozen of what are called autosomal STR (Short Tandem Repeat) markers. This is what, for example, law enforcement agencies in most countries use, and what's brought into play in legal paternity cases. The issue is that it can do an excellent job of identifying an individual or proving the closest degrees of relationship (i.e., parent/child or full sibling), but these types of tests can't help at all with establishing a relationship to a long-deceased ancestor. In order for it to have been applicable even for your father, both he and the Kaiser would have had to have taken the same type of test. Besides, these are typically more expensive than the testing we do for genealogy.