Yes. Use the recording function of the DJ application connected to the DDJ-FLX6.

[rekordbox]

Click the [REC] button at the top left of the rekordbox screen to display the recording panel in the middle of the screen.

Click the [REC] button in the panel to start/stop recording.

For details, see [Recording] in [Performance mode] in the rekordbox Instruction Manual.

See the rekordbox Instruction Manual [here]

[For Serato DJ Pro]

Click the [REC] icon at the top left of the Serato DJ Pro screen to display the recording panel in the middle of the screen.

Click the [REC] button in the panel to start/stop recording.

For details, see the Serato DJ Pro software manual.

See the Serato DJ Pro software manual [here].