For info, flashpoint is not a physical property of a liquid that can be measured in the same way as boiling point or freezing point. Flashpoint is the result of a flashpoint test; the equipment and manner in which the test is undertaken will all affect the result, hence the same oil tested in different flashpoint apparatus will give different answers!
That there are so many different test apparatus is the result of different industries, in different countries, over a long period of time, all attempting to answer the simple question "what is the safety hazard of this liquid"? Abel closed cup and Pensky-Martens closed cup date from late 1800s, Tag close cup and Cleveland open cup date from the early 1900s, to which we can add the more modern equilibrium and rapid equilibrium test methods.
Flashpoint is essentially the lowest temperature of a liquid at which vapours from a test sample combine with air to give a flammable mixture that will 'flash' (i.e. explode) when an ignition source is applied.
Firepoint is the lowest temperature of a liquid at which vapour combustion and burning commences when an ignition source is applied and thereafter is continuous even after the removal of the ignition source.
There are two general classes of flashpoint test: open cup and closed cup, and as the name implies the vessel containing the test sample is either open or closed prior to the ignition source being applied.
The open cup was initially developed to assess the potential hazards of liquid spillage. In this test, a sample is introduced into a cup that is open at the top. As the cup and liquid are being heated, an ignition source is passed horizontally over the surface of the liquid to test if the vapours 'flash'. If the test is repeated at increased temperature, a point may be reached when the sample continues to burn without further application of the ignition source - the firepoint.
A closed cup test contains any vapours produced and essentially simulates the situation where a potential course of ignition is accidentally introduced into a container, such as a fuel tank or oil sump. The test cup has a close fitting lid that can be opened to allow air in at the same time as the ignition source is applied. Note that firepoint testing is not undertaken in closed cup apparatus.
It is no surprise, of course, that open cup tests usually give higher flashpoints than closed cup tests.
Quite often, the choice of which test method or test standard to use is set out in the product specification or detailed in the regulation you are trying to meet. For example, UN Recommendations on the Transport of Dangerous Goods specifies the following standards as being acceptable for non-viscous liquids; 4 US standards, 2 British standards, 1 Russian standard, 6 Dutch standards, 3 German standards and 3 French standards. To quote Mark Twain from Huckleberry Finn "you pays your money and you takes your choice!"
Here's a list of the common tests from a commercial flash point testing