flatten_tree.rb

# Definition for a binary tree node.
# class TreeNode
#     attr_accessor :val, :left, :right
#     def initialize(val = 0, left = nil, right = nil)
#         @val = val
#         @left = left
#         @right = right
#     end
# end
# @param {TreeNode} root
# @return {Void} Do not return anything, modify root in-place instead.
def flatten(node)
  if node.nil? || (node.left.nil? && node.right.nil?)
      return
  end
      
  unless node.left.nil?
     flatten(node.left)
     right = node.right
     node.right = node.left
     node.left = nil
     current = node.right
     while current.right
        current = current.right 
     end
     current.right = right
  end

  unless node.right.nil?
     flatten(node.right) 
  end
    
  return node

end

Post order traversal:

# Definition for a binary tree node.
# class TreeNode
#     attr_accessor :val, :left, :right
#     def initialize(val = 0, left = nil, right = nil)
#         @val = val
#         @left = left
#         @right = right
#     end
# end
# @param {TreeNode} root
# @return {Void} Do not return anything, modify root in-place instead.
def flatten(node)
    if node.nil?
        return
    end
        
    flatten(node.left)
    flatten(node.right)
    
    if node.left
        temp = node.right
        node.right = node.left
        
        current = node.right
        while current.right
            current = current.right
        end
        current.right = temp
        node.left = nil
    end
    
end

def flatten(node)
  if node.nil? 
      return
  end
      
  if node.left
     flatten(node.left)
     right = node.right
     node.right = node.left
     node.left = nil
     current = node.right
     while current.right
        current = current.right 
     end
     current.right = right
  end

  if node.right
     flatten(node.right) 
  end
    
  return node
end

Refactored version of first solution.