how to set the properties of an item frame to a custom one

If you're referring to having the item frame hold an item a certain way, this can be done while making a custom model same way one would edit how it looks on the head or in hand.
Though, based on how you worded it, I assume you want the dish item to act as an item frame. I don't think is this really possible in simple ways. I do have an idea for a more messy sort of way, though.

Item frames use entities for their blocks. And as such you could probably have the dish item spawn an entity instead of a block. Since only zombie and biped models can hold items, the entity should be using a zombie or biped model. The texture should only be on the part that should be shown, for example, the face of the model. The rest should be transparent. Have it so when right clicking the entity it sets the entities head item or held item to whatever the player is holding.
Some other things should be set as well, AI should be disabled, for example.

Of course, this solution has a huge amount of its own problems. so I don't think it would be worth it. I would recommend finding an alternative to having the item working like an item frame.