To solve this problem, we first need to define the variables and the objective function. Let's denote:
- $x_1$ as the number of hours the mall kiosk operates.
- $x_2$ as the number of hours the flagship store operates.

The objective is to minimize the total cost, which can be represented as $150x_1 + 500x_2$.

Now, let's formulate the constraints based on the production capabilities and demands:
1. The mall kiosk produces 5 small gift boxes per hour, and the flagship store produces 10 small gift boxes per hour. The demand for small gift boxes is at least 80.
   - $5x_1 + 10x_2 \geq 80$
2. The mall kiosk produces 6 medium gift boxes per hour, and the flagship store produces 15 medium gift boxes per hour. The demand for medium gift boxes is at least 100.
   - $6x_1 + 15x_2 \geq 100$
3. The mall kiosk produces 2 large gift boxes per hour, and the flagship store produces 9 large gift boxes per hour. The demand for large gift boxes is at least 50.
   - $2x_1 + 9x_2 \geq 50$

All hours of operation must be non-negative:
- $x_1 \geq 0$
- $x_2 \geq 0$

Now, let's represent this problem in the requested symbolic notation:

```json
{
    'sym_variables': [('x1', 'hours mall kiosk operates'), ('x2', 'hours flagship store operates')], 
    'objective_function': '150*x1 + 500*x2', 
    'constraints': ['5*x1 + 10*x2 >= 80', '6*x1 + 15*x2 >= 100', '2*x1 + 9*x2 >= 50', 'x1 >= 0', 'x2 >= 0']
}
```

And here's how you can solve this problem using Gurobi in Python:

```python
from gurobipy import *

# Create a new model
m = Model("candy_production")

# Define the variables
x1 = m.addVar(lb=0, name="mall_kiosk_hours")
x2 = m.addVar(lb=0, name="flagship_store_hours")

# Set the objective function
m.setObjective(150*x1 + 500*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(5*x1 + 10*x2 >= 80, "small_gift_boxes")
m.addConstr(6*x1 + 15*x2 >= 100, "medium_gift_boxes")
m.addConstr(2*x1 + 9*x2 >= 50, "large_gift_boxes")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Mall kiosk hours: {x1.x}")
    print(f"Flagship store hours: {x2.x}")
    print(f"Total cost: {m.objVal}")
else:
    print("No optimal solution found")
```