SY isn't recognised by BS7671 as it isn't manufactured to any recognised British standard. You would need to consult manufacturers data.
Also it's use is classed as a departure from BS7671.
You are half correct here, the BS 7671 does not rule on cable standards but it may say cables should meet BS standards, I can't quite recall now, it is the '
BS EN 50525-2-11' that I think you may be referring for cable standards which has no provision for the braiding thus the cable isn't covered and by default is not compliant, however it does not stop you using it but you need to do a write up on it suitability and use and why you selected it instead of a compliant cable, this also means any premature failure, injury or death resulting from the cable been used is on the shoulders of those who selected it for use and it cannot be turned on the manufacturers as easy.
SY is not an alternative for flex.
SY screening should always be earthed but not relied on as a fault path or used as an earth for low voltage installations.
SY should not be used outdoors, it has very low UV tolerance which will quickly breakdown the sheath.
SY is a screened control cable and careful consideration must be used before you use it for anything else, its outer clear sheath is very soft and offers little protection for the braid, its braid will rust/corrode quickly if moisture gets in too, if fact this is by design as it found a use in the railway underground network where routine checks for cable damage were made easier as the sheath was see through and all you needed to look for in the damp conditions is rusty sections of braid.
I often despair at the amount of this stuff I have seen misused and in some cases created a lethal scenario, 3 times I have seen this used as extension cable with the braiding not earthed and live due to damage along the cable, I throw this stuff in the bin at every opportunity when I see it used in this way, for the OP - some HO7RN-F will be more than suitable and resistant to many of the oils and chemicals it will be exposed to unlike standard PVC.