This pretty plate is decorated with a Japanese iris hanashōbu (Iris ensata) a particular garden favorite in Japan and much painted in the decorative arts, too. The artwork style is in keeping with a type of woodblock printing that became fashionable in the 1920s and 1930s called Hanga. Simple but bold botanical subjects that filled the whole page but with deliberate areas of empty negative space to emphasize the subject matter. So I would date your dish to the 1930s.
It was made in a small and somewhat obscure pottery called Hakenomiya located near the city of Kumamoto in Kyushu, the southernmost of the islands of Japan and very much the birthplace of pottery and porcelain there.
The kanji script on the tomobako (the wooden earthquake box) says:
Which translates as "Hakenomiya Kiln"
and to the left of that,
絵皿 meaning "dish"
Two red seals, one for the Hakenomiya pottery and the other the rakkan (personal seal) of the decorating artist who painted the iris.
The incised mark in the back of the plate is for the individual who made the dish itself:
純 "Jun" -which also means "genuine, purity and innocence".
All of this is of curiosity value. In other words, it's great to know, but it doesn't add to or detract from the value of the item. There were thousands of kilns operating in Japan at the time and tens of thousands of decorators, of which only a very small number were, or are, collected "names". They would be obscure even to the Japanese, let alone in the West. In fact this decorator could well have been just a hobby artist or china painter rather than a full time professional.
So all-in-all, it's an interesting item as it represents very nicely a particular moment in the history of the ceramic arts in Japan just before World War II, after which nothing would ever be the same again.
As for value, not a great deal, though having the original tomobako does elevate it from the ordinary, they are so often lost or discarded. If you were to see your plate and box for sale in an antique store, together they would have a full retail price of about $150. This is also the replacement value for insurance purposes.
Expect to get 30% - 40% of this if you were to sell at auction or on line (eBay etc).
I do hope this helps! And many thanks with your patience and perseverance with the pictures!