We don't know what kind of reporting or business relationship is involved here, but I can almost assure you, at the very least - this practice will be frowned upon, and more than likely it could be in violation with a contractual relationship you or you company have with an employer or other company, it could be against policy, it could be illegal.
The reasons are obvious - there are serious conflict of interest considerations. You are benifiting monetarily from travel (yes there is that component with any travel and frequent flyer points, but here we are talking hard cash which will far exceed the value of an FF credit points) - thus you are being encouraged and rewarded for spending your employees or customer money beyond stricly business need considerations, not only that, you are being encouraged and rewarded to pick the most expensive route and time to travel to get the greatest reimbursement. Can you see the control weakness here? That's why, for all but those very small or loosly controlled companies, this is forbidden.