My understanding is that the concierge (they actually refer to this as Personal Shopper) service can only be used to get "things" Dream rewards ... nothing travel related. I think the only way you can "pay" the fees for flights with miles is if you have the AMEX Reserve credit card (possibly the Mastercard fancy pants card too?)
Several of us have used the Personal Shopper recently to get tickets for Disney & Universal, both regular gate tickets and party nights and someone snagged a computer this way as well. You can either start the process thru online chat or phoning to the ONYX line OR I even did it thru Facebook Messenger on Canada Day! You let them know what you'd like them to source for you and you'll get a quote within 4- 10 business days. You can then accept it and tell them to move forward on the item and POOF, you get whatever it was you've asked for and the miles disappear.