Don't know if it is still running (or again running) but there is supposed to be a train once a week between Uyuni and Calama in northern Chile. From there you can take a bus to Iquique. The train takes about 24 hours and delays are not unheard of. Still, like I said, I wouldn't bet on it, but that is the most direct (though much longer in time) route. Otherwise, if you want, go for a 3-day trip between Uyuni and San Pedro de Atacama and take the bus from there. That way you will actually see something as well, or are you in a hurry?
But like you said, the most direct normal route would be a train/bus to Oruro or even La Paz and travel from there by bus to northern Chile (probably via Arica, but not sure) and down to Iquique.