Even if the Klingons reverse engineered the technology of another culture, that would still require a decent theoretical understanding of the principles involved.
They don't have to reverse engineer it, though. Conquered civilizations aren't always destroyed. "You will now teach us about this technology. You will build this technology for us." etc...
By the 24th Century the Klingons are also allies of the Federation. I'm sure trade agreements exist. Heck, the United States sends ships and planes to all kinds of other countries, even ones that aren't as favorable allies as others.