There are several ways to set a custom application data folder.
1. The preferred way is during installation.
During the installation of FlashFXP, on the "Setup Type" page uncheck  "Individual Settings and Site Profiles" and select "custom" setup type,  click the Next button, Select the desired components, click the Next  button, Set the program installation location, click Next the button,  Now you can set a custom program data folder location, you'll want to  set this to the folder you are syncing via DropBox, Click the next  button, Review your settings and click the Install button.
2. Via the command line
FlashFXP.exe -datafolder="<path>"
(anytime FlashFXP is run without this command switch the data folder  reverts back to the one that was set during the installation.)
3. You can set a custom path for each individual data file via the registry.
 
Additional information regarding this method can be found in the help  found under the section Power-user Settings > Custom data file  locations. (
online help file)
* These settings are configured via the windows registry and  requires administrative permissions.  
 
* These settings do not apply to the USB portable or U3  portable editions of FlashFXP.
On 32-bit versions of Windows the location is:
 
HKEY_LOCAL_MACHINE\SOFTWARE\FlashFXP\4
  
 On 64-bit versions of Windows the location is:
 
HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\FlashFXP\4
Add a new 
String value (REG_SZ) with the name as (insert the file-name) and with a value set to the desired location of the data  file.
  
 You can use system environment-variable like 
%ALLUSERSPROFILE% or
%APPDATA% in the value. i.e. 
%ALLUSERSPROFILE%\flashfxp\4\