I think I'm the only one roblox player who ask for this. But maybe not?

Put this script inside a Script inside your dialog and make a dialog choice named "Hat";

HatId = 1708345137 -- Change this to the Had Id that you want
script.Parent.DialogChoiceSelected:connect(function(Player,Choice)
    if Choice.Name == "Hat" then
        local Hat = game:GetService("InsertService"):LoadAsset(HatId)
        Hat:GetChildren()[1].Parent = Player.Character
        Hat:Destroy()
    end
end)

How it works: So first of all, this event activates when the player chooses a dialog choice. Then we check if the choice's name is "Hat". And if the player chooses "Hat" then the script will active. I used InsertService to insert the Hat by it's AssetId. But with InsertService it inserts the item inside a model. So since the Hat is inside a model, our "Hat" variable is equal to the model right now. So we just need what is inside the model, which is the hat. So we do GetChildren(). That function returns a table of all children inside our model.To get the hat inside the model we would use GetChildren()[1]. And now we set the the first child's (the hat) parent to the Player's character. And lastly, since we don't need the model anymore we just destroy is with Hat:Destroy().

Now if you have a hat in your game you want to give to the Player do this: (Make sure the Hat's Handle is not anchored!)

Hat = game.Workspace.Hat -- Set this to the hat object
script.Parent.DialogChoiceSelected:connect(function(Player,Choice)
    if Choice.Name == "Hat" then
        Hat:Clone().Parent = Player.Character
    end
end)