I would recommend to book DL operated by DL and use FB miles to upgrade. I believe you have a higher chance of having an upgrade availability on DL/DL rather than DL/AF, because AF would unlikely to offer J seats for upgrade given their aggressive paid upgrade policy.

I tried this trick in the past on "pure" DL flights (YCA gov fares on DL on ATL-SCL), unfortunately it didn't work because there was no availability at those particular flights.

An FB agent once explained me on phone: if you want to check the business class upgrade award availability on a DL flight, try to check whether FB web-site offers you an award ticket on the same DL flight. If it does, give us a call right away and request an upgrade before it's too late.

good luck