Welcome to FT, jessyj! I'll try to summarize the good responses above and make it a bit less Flyertalk-y I know sometimes it can get a bit confusing.

The problem you're facing
The problem you're facing as outlined above is a (likely) result of one of two things:
1. There is a mismatch of information between your AMEX account and your FlyingBlue (FB) account. OR
2. FlyingBlue is seeing "hmm this account was created and is immediately transferring miles without any logged flights, this might be fraud" and flagging as such.

What is being suggested
You'd start by looking into (1) and making sure information matches exactly (you mentioned "business" — so maybe another layer to look into). If (1) is all good (if confirmed as such by FB or Amex) then you want to look into (2).

Basically on (2) you need to show FlyingBlue you are a legitimate user and not trying anything fraudulent. Although you can "appeal" the easiest way to do it is to credit points/miles/activity to the program (i.e. credit to FlyingBlue) any activity that is genuine. This can take the form of:
1. Flights with AirFrance, KLM;
2. Flights with partner carriers (either part of SkyTeam, whose example is Delta, or other partners);
3. Other legitimate credits (e.g. if you link your Accor/ALL (accorhotels.com) account with FlyingBlue and have a stay at an Accor property you'd earn FlyingBlue points.

Essentially the easiest path and the one being suggested seems to be (2) since you mention you have a flight coming up with Delta. Since Delta is a FlyingBlue partner (for being part of SkyTeam) you can credit any Delta flight to your FlyingBlue account. This means changing your SkyMiles in your booking to your FlyingBlue (AirFrance/KLM) number. Do note this means:
- You will earn miles for that flight on FlyingBlue not SkyMiles;
- You will not get any benefits on the flight that you'd normally get if you do have status with Delta unless you show the card (for lounge, priority etc);

Then you wait for the miles to post to your FlightBlue account. When you see it going above 0... it's done!

The hope is that you then (after) try to transfer the points again and FlyingBlue will see "ok this user actually travelled, seems legitimate and now is trying to transfer points - let it go through".

Hope it helps and safe travels!