They aren't listed as an eligible subsidiary at ba.com:
Japan Airlines
•Flight prefix: JL, JC, J-Air, NU
•Eligible subsidiaries include: JAL Express (JC), J Air (JL), Japan Transocean (NU)
•Minimum Avios*: N/A
Redemptions on Japanese domestic flights may only be booked two months from the date of return flight and only in the economy cabin. This restriction does not apply to domestic flights booked in conjunction with international flights.