Why do my under-cabinet lights flash when two sets are plugged into the transformer?
Per IKEA, the 24" OMLOPP LED bar draws 7.7W of power.  A single 10W transformer will not be enough to provide power to two 24" bars at full brightness, despite the included transformer having slots for multiple bars to be attached.  You will need one of the larger ANSLUTA transformers (seemingly also available in 30W form) or to chain multiple transformers together (also permitted per IKEA).

In fact, it is noted in the reviews that the included 10W transformer, being unable to power two 7.7W bars, will induce a strobing effect if you exceed the rated power.  Presumably, the 10W transformer can provide enough power for multiple smaller bars and is simply the transformer included with all products in that line.