In appears that the synthetic procedure for preparation of iron(II) oxide from iron(II) oxalate has been first described by Günther et al. [1] and subsequently summarized in Brauer's Handbook of Preparative Inorganic Chemistry [2, p. 1497]:
Iron (II) Oxide
I.
$$\ce{\underset{143.8}{FeC2O4} = \underset{71.8}{FeO} + \underset{28.0}{CO} + \underset{44.0}{CO2}}$$
Thermal decomposition of $\ce{FeC2O4}$ yields pure $\ce{FeO}$ only under specific conditions.
The decomposition is carried out in a quartz vessel (Fig. 332) whose lower section is kept at $\pu{850 °C}$ by means of an electric furnace.
The joint is surrounded by a water-cooled lead coil or a rubber hose.
The nascent gases should be removed as quickly as possible; for this reason, the reactor is connected to two parallel mercury pumps and a good forepump; the gas is carried into two liquid-nitrogen-cooled traps containing activated charcoal.

Fig. 332. Preparation of iron (II) oxide.
The starting $\ce{FeC2O4}$ $(\pu{0.5 - 0.8 g.})$ is placed in the small bulb above the quartz vessel, and the water of crystallization is completely vaporized by heating in vacuum for 12 hours at $\pu{200 °C}.$
The bulb is turned in the joint, and the $\ce{FeC2O4}$ drops into the heated lower section of the reactor where it is rapidly decomposed to $\ce{FeO},$ $\ce{CO}$ and $\ce{CO2}$ (the decomposition is complete in about 20 seconds). The product $\ce{FeO}$ is retained by a quartz wool plug, which must be loose enough to prevent a buildup of pressure during the decomposition.
The furnace is now removed and the hot quartz tube is chilled as rapidly as possible in cold water, since $\ce{FeO}$ is unstable in the range of $\pu{300-560 °C}$ and decomposes according to:
$$\ce{4 FeO = Fe3O4 + Fe}$$
(this decomposition proceeds most rapidly at about $\pu{480 °C},$ but
ceases below $\pu{300 °C}).$
The above procedure yields a jet-black product, readily soluble in dilute acids; it is rapidly oxidized in air, but does not ignite.
Alternatively, iron(III) oxide can be reduced by iron to iron(II) oxide [2, p. 1498]:
II. The preparation from stoichiometric quantities of commercial $\ce{Fe2O3}$ and reduced iron can also be recommended.
The mixture and a few drops of water are sealed into a preevacuated quartz tube, heated for about three days at $\pu{900 °C},$ and quenched in cold water.
$$\ce{Fe + Fe2O3 ->[\pu{900 °C}] 3 FeO}$$
Iron(II) oxide can also be produced from iron(III) oxide reduction by carbon monoxide at the temperature range between $\pu{500 °C}$ and $\pu{600 °C}$ (adapted from [3, p. 415]):
$$
\begin{align}
\ce{3 Fe2O3 + CO &->[\pu{400 °C}] 2 Fe3O4 + CO2} \\
\ce{Fe2O3 + CO &->[\pu{500-600 °C}] 2 FeO + CO2} \\
\ce{Fe2O3 + 3 CO &->[\pu{700 °C}] 2 Fe + 3 CO2}
\end{align}
$$
as well as by thermal decomposition of magnetite [3, p. 415]:
$$\ce{2 Fe3O4 ->[>\pu{1538 °C}] 6 FeO + O2}$$
References
- Günther, P. L.; Rehaag, H. Über Die Thermische Zersetzung von Oxalaten II. Mitteilung. Darstellung von Reinem Ferrooxyd. Z. Anorg. Allg. Chem. 1939, 243 (1), 60–68. https://doi.org/10/cqzgk8. (in German)
- Handbook of Preparative Inorganic Chemistry, 2nd ed.; Brauer, G., Ed.; Academic Press: New York; London, 1965; Vol. 2. (Archive.org)
- R. A. Lidin, V. A. Molochko, and L. L. Andreeva, Reactivity of Inorganic Substances, 3rd ed.; Khimia: Moscow, 2000. (in Russian)