Should I rotate the tires on a (grown-up) trike?
Swapping the tires around (or if they have some sort of quick release axles, the wheels) isn’t going to do any harm, and will prolong the useful life of the tire if they are contacting the ground at an angle. 

How often to do it is hard to tell. Depends on how many miles you ride / week, mass of you plus bike, roads surfaces etc. I’d probable swap tire around when I begin to see some wear.