The thing to bear in mind here is "targeted" or "spot reduction" fat loss is a myth. A myth that sells a lot of gimmicky exercise equipment. There's no special exercise that will make you burn fat specifically from your chest. So the ticket here is to do something that will make you burn fat, some of it may be from the chest area.
If you look at endurance athletes they tend to have rather low body fat, so I'm thinking that works well to burn fat. Other things to keep in mind are caloric deficit (if one eats maintenance, or surplus calories one still burns fat, people burn fat all the time, but it gets replaced) and body fat distribution patterns. Estrogen, and T levels below male-typical, tend to make bodies more likely to distribute some fat to the chest area. Bottom line is, if you want to go this route you'll need to read up on general fat loss.
Something else to think about. Binding comes with risks too, and the longer one binds, the more likely problems become. Barring a need for revision, top surgery is something people generally only have to do once. If fat loss doesn't give you the results you're looking for, consider consulting with some top surgeons. They're the professionals, they would be able to discuss risks and risk management with you.
