This matter has been debated for a long time. One thing that was not mentioned above is that flooding causes a reduction in respiration of roots. Although water is not, theoretically, actively (with energy expenditure) absorbed, you must also keep in mind there are aquoporins and live membranes that may be affected by low ATP availability. Therefore, low respiration may have an impact on water uptake, which eventually may reduce mesophyll hydration, and, consequently lead to low stomatal conductance (gs).
Now, if you have any chance or are still interested in the matter, please check a recent paper I have attached. It is interesting because the species involved in this study naturally occurs in flood-prone areas, like riparian and gallery forests. Therefore, the species treated in the study is not expected to "suffer" from flooding conditions. However, one of the first symptoms observed in the study was low gs.
And finally, just a correction: transpiration is not an osmosis phenomenon, but it occurs following the diffusive laws (diffusion!)
under flooding condition usually oxygen is rarely available for root respiration, under such condition ROS especially hydrogen peroxide together with some phytohormones such as ethylene and nitric oxide produced. These signals which are mostly secondary messengers or phytohormones translocate to the leaf. In the guard cells of the stomata usually these signals contribute to the loss of water from the guard cell and as a result shrinking of the guard cells and finally stomatal closure. Also our research showed that in flooding conditions the level of abscisic acid as the main phytohormone inducing stomatal closure, increased in the leaf but not in the root which can be another explanation for stomatal closure under hypoxia conditions.
the mechanism of stomatal closure under flooding condition is also probably hydraulic. Flooding increases soil water potentials (more negative because of the respiration issues noted in the answers above) which affects negatively whole-plant hydraulic conductance inducing stomatal closure, because of the tight coordination between liquid- and gas-phase water transport.