Hi LeCuvier,
You are on the right way. Open the default.lua file from ...\Eagle Dynamics\DCS World\Mods\aircraft\FW-190D9\Input\FW-190D9\joystick\ folder. Then add next two strings in the --flaps section of the file.
{combos = {{key = 'JOY_BTN22'}}, cockpit_device_id = devices.CONTROL_SYSTEM, down = device_commands.Button_1, value_down = 1.0, up = device_commands.Button_2, value_up = 1.0, name = _('Toggle Flaps Up'), category = _('Flight Control')},
{combos = {{key = 'JOY_BTN23'}}, cockpit_device_id = devices.CONTROL_SYSTEM, down = device_commands.Button_3, value_down = 1.0, up = device_commands.Button_2, value_up = 1.0, name = _('Toggle Flaps Dn'), category = _('Flight Control')},
Don't remove any other strings from there.
Updated file will be available in next update.
Thank you for your post!