Can cooking oil be incinerated providing the manufacturer permits it ?

Cooking oil can be burned in an incinerator, provided it does not get into bilge/sludge systems.

This would mean providing an incinerator day tank which only goes to the incinerator and there is no water  drainage facility back to the engine room bilge system.

The reason for these measures is that oily water separators are not designed for use with cooking oil. Doing so could cause malfunction or put a film of oil on the 15 ppm alarm giving incorrect readings. Even if the system works, there could be potential problems with port state control.

In view of the two above points, it is recommended that used galley oil be kept separately for landing ashore, along with other garbage and a certificate obtained, thereof.

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Putting used oil in the oily bilge system means putting it through the Oil Water Separators (OWS). This also means that oil specified in MARPOL Annex I is being mixed with Annex V. If this is the case, the vessel is running the risk of a port state control detention. The OWS unit and 15 ppm bilge alarm are not approved to treat used cooking oil, which may cause a malfunction or misreading of the discharge of oil.
OWS are approved according to Resolution MEPC.107(49)

“Revised Guidelines and Specifications for Pollution Prevention Equipment for Machinery space bilges of ships”.

Each system is tested against three grades of test fluids (Section 1.2.4 of MEPC.107(49)) which are: A) Marine Residual Fuel Oil; B) Marine Distillate Fuel Oil; C) a mixture of A, B and detergent.

The system is not tested against cooking oil in order to be MEPC.107(49) approved. This however does not mean that the OWS could not handle cooking oil. An OWS, in practice, should be able to handle cooking oil – however, the current standard of testing does not include it. And if a problem arises, it may lead to no protection from the actual standard of testing.
It is recommended that it should be kept separate and returned to the shore. All the records in the MARPOL Annex I Oil Record Book will need to correspond with MARPOL Annex V Garbage Record book for discharge to the shore.