The Scots is a Regimental Insignia, therefore worn on the right arm. The TRF is a Brigade insignia which is worn on the left arm, just like the remainder of 16AA bde. However when posted away from 5 Scots the TRF should not be worn. Happy Now!
Whatever their penchant for badges, my lad was on Herrick 8 with them, as part of their Mastiff Coy, and said they were superb lads from top to bottom. He made many great friends, loads of whom are still in contact with him. Titaniums Mash man...Si the Pie!! To answer the question though, the Scottish regiments are still allowed to keep their original identities to a certain degree, even though they have all been amalgamated under the RRS banner. So each Btn has a slightly different TRF, to reflect their different old regiments, when not in Bde? Or at least that's how i understood it to work, but i could be very wrong?
The Thin Red Line TRF is just worn by 5 SCOTS in 16 Bde (this is an authorised badge for 5 SCOTS in 16 Bde only - like the PWRR TRF worn in addition to the Tiger, all those years ago). All SCOTS soldiers wear the SCOTS TRF (Lion Rampant on Saltire). The difference between the Bns in the Royal Regiment of Scotland (SCOTS, not RRS) is denoted by the different hackles:
1 SCOTS - Black
2 SCOTS - White
3 SCOTS- Red
4 SCOTS - Blue
5 SCOTS - Green
6 SCOTS - Grey
7 SCOTS - Purple
Note that 2 SCOTS (also in 16 Bde does not wear another TRF).
Edited to add that 1 R IRISH also have a TRF in 16 Bde in addition to their clover badge.