Coker LPG caustic treatment is normally for removal of mercaptans and COS through a UOP Merox unit or a Merichem Thiolex unit. The spent air is typically routed to a fired heater to be combusted. In your case you use the incinerator of the SRU, which is fine.
I have seen this stream routed to a flare as the spent air stream was not near any fired heaters. My preference is to not route this stream to a flare, but find a heater or incinerator close to the caustic treating unit and route the spent air to that destination. I do not like to put any air stream into the flare header, which is my main objection to this routing. Additionally, whatever is plugging the spent air line will also deposit in the flare header and restrict the flow of hydrocarbons out the flare.
Do you have any calcium or magnesium (hardness) in the water used to dilute the caustic to proper densities? Hardness can cause emulsions in the caustic and calcium salts can be very difficult to remove. Entrained caustic with calcium in it could be the source of the deposits. Have you analyzed them?