I know former Royals in the RN can wear the green beret with the covetted RN beret badge (subject to local restrictions) & that the Commando Dagger can be worn on the sleeve of the number 1 (parade) uniform, but not heard of the Royal Navy Commando flash being worn on anything other than MTP, but that's usually for AACC qualified ratings rather than ex-Royals.
BR3, Chapter 39, Article 3925, paragraph g refers:
3925. Insignia and Badges Worn with No 4 RN Personal Clothing System (No 4 RNPCS)
..... g. Shoulder Flashes. Wearing of shoulder flashes is authorised for personnel qualified to wear ‘RN Commando’ and ‘Bomb Disposal’. Qualified RN EOD personnel are authorised to wear the EOD operator Joint ‘Bomb’ badge (red bomb on blue background) and qualified members of the Submarine Parachute Assistance Group are authorised to wear ‘Parachute Wings’; these are to be worn centralised on the right arm, the top of the badge being 6mm below the bottom of the trade badge. Communicators who have served with 148 Bty and other niche groups who have been awarded ‘Parachute Wings’ are authorised to wear them.