"in reflecting" is correct and usable in written English.
You can use it when discussing a period of consideration or contemplation. For example, "I spent the night in reflecting on my future."
Then, departmental politics kicked in, reflecting widespread rivalries between career officials and political appointees.
In Reflecting Absence, both footprints would be turned into 30-foot-deep reflective pools, edged with curtains of falling water.
Ever-blue sky glistens in reflecting pools.
In reflecting on his sport, Parks retained his boyish enthusiasm.
Water, whether trickling or in reflecting pools, became a hallmark.
In reflecting on the arguments in the China debate, I don't see the difference.
In reflecting on the Battle of the Bulge, Mr. MacGillivary minimized his heroics.
Schilling seemed to take pleasure in reflecting on his previous life of leisure.
But, he said, each does its job in reflecting presidential character.
I'm much more interested in reflecting what the author intended rather than the press office.
Rucker, for his part, seems largely disinterested in reflecting on his legacy as a black pioneer.
