Well, that clears up a lot, in my mind! Smalltowing is something I know about- I'm doing it myself and have a fair understanding of the limitations of non-truck type vehicles.
You're probably familiar with this: I found the towing guide for the Flex
-assuming yours is a 2013 model.
According to that, your "actual" hitchpoint weight
limit is 200 pounds, but that with the tow package including W/D hitch, the trailer tongue
can be as heavy as 450 pounds. Point being that it's important to differentiate between "hitch weight"(vehicle) and "tongue weight" (trailer)
What those numbers mean is that a W/D hitch properly adjusted will transfer all but around 200 pounds of tongue weight
off the hitchpoint/rear of the tug. Some goes to the front of the vehicle, and some back to the trailer wheels.
The total weight placed at
the hitch with a W/D can't exceed 450 pounds, so the math question as to how much of the 100 pounds you're adding with a bike rack will be "transferred" is really a moot question.
You say your present tongue weight is "about 400 pounds"- what trailer are you towing, and how much does it weigh loaded ? I ask because you're obviously very near your tongue weight limit, and I wonder if there's any wiggle room in the tongue weight, which for stability must be about a minumum of 10% of total trailer weight.