You are setting your self up for failure flying from two SkyTeam hubs/focus cities on OneWorld. At a minimum you will need three segments (FLR-European hub, OW TATL, American hub - CVG) and the odds of them showing up on a single search in J/F are slim at best in the winter and extremely unlikely during the summer. You are unlikely to get four-segment searches to show up in any normal tools.
I would HIGHLY recommend that you buy a trip pass at AwardNexus for the purpose of this trip, or else consult with a paid award booking service unless you are willing to put in a ton of legwork on this.
Barring that, there are a couple of strategies:
A. Use UR points to transfer to United. Their online award search is actually pretty easy and friendly to find award space. Use MR to transfer to DL (or possibly FlyingBlue or Alitalia). Do you have enough miles in either program for a TATL J ticket for 2 people?
B. Consider a train ride as suggested by
@italdesign or a short paid/Avios hop to a better European starting point. Is there any other city you might be interested in spending a night? ZRH? MXP? BCN?
C. Break down the trip into its possible routes
1. Go to
wikipedia and see which airlines actually serve FLR, and whether any of them are One World. See which OW hubs in Europe are served. I see the possibilities are
--AB to DUS or STR
--BA to LON
--IB to MAD
--Vueling to lots of places, but I'm not sure you can get space with AA miles. If that works, you will open up a lot of options.
2. Which American hubs have
direct service to CVG? (Wikipedia)
--Charlotte, Chicago–O'Hare, Dallas/Fort Worth, Miami, New York–JFK, New York–LaGuardia (begins January 5, 2016), Philadelphia, Washington-National
3. So now we know that you are looking for TATL OW service from MAD, DUS, or STR to CLT, ORD, DFW, MIA, NYC, PHL, DCA. Go to aa.com...where we fly...show a larger map. (this takes you to aa.innosked.com) Figure out which OW routes exist. Uncheck 'Add AA connections' but leave Partners checked.
DUS-MIA/NYC/ORD on AB
MAD-CLT/ORD/DFW/MIA/NYC on IB or AA
The good news is, that only leaves 8 routes to search one-at-a-time. The bad news is, there are only 8 flights that are possible routes for you to use.
4. So now we know you are looking for flights ex-DUS or ex-MAD to an AA hub. Use AA.com or Qantas to search for OW availability on the nonstop TATL flights you are interested in XXX-YYY. Then go back and fill in the positioning flights FLR-XXX and YYY-CVG.
--The problem you will hit with AA is that you won't know if a route includes BA until you click through, and AA will tend not to show awards in J if a single segment is missing.
--The problem you will hit with QF is that they will show an award in J, and then you will click through and find that the TATL is in Y.
--The problem with BA is that if there is a possible BA route, they will often omit inventory on OW partners.
--Consider Alaska Air award searches, they clearly break down AA versus BA and clearly show 'Mixed Cabin inventory' when it is a mix of Y and J (but they don't include Iberia routes)
--I would get a paid EF subscription to search for award availability on those 8 routes on IB and AA. But if you rarely book your own awards, between Award Nexus and/or EF, you are looking at close to the cost for an award booking service, not to mention time required to learn those tools.
5. Also, it will be helpful to search for awards for just one passenger, you might actually find some of those and that will give you a starting point. Then you can book the first seat and set up ExpertFlyer Alerts for the other seat.
Good luck
ETA: Just realized I omitted a huge option, you can do BA FLR-LHR and then AA metal LHR-AA hub. Still the same principles apply, you would need to search one-by-one for LHR-CLT, ORD, DFW, MIA, NYC, PHL, DCA. That one is actually pretty easy to do on AA.com, you can restrict the carrier preference to only AA and Amercian Eagle. You will still incur hundreds of extra dollars in UK departure taxes, but it's not as bad as BA fuel surcharges. Also throw in LHR-CVG (restricted to AA only) and see if there is any married segment logic that opens up two seats on a single flight.
