The only lounge I know of at BWI is the AirSpace lounge in Terminal D. your AmEx Platinum will get you in and it is open for all scheduled departures but I don't believe FL uses that terminal so you would have to deal with security again to get to it and then to your gates. Probably not worth it.

I don't see any other lounges listed on the BWI amenities map: http://www.bwiairport.com/en/shops/shop-dine.