Good luck oomis!
I’m not sure how well DY’s latke recipe above will hold together with no eggs. I’d suggest that in addition to the little bit of flour you add a small amount of matzo meal, and let it sit in the bowl for a minute or two to come together. Make the latkes small, and make sure that the oil is hot enough to make them sizzle as soon as they’re in the pan.
Let us know what happens!