In a large bowl, add shredded chicken, mayonnaise, and softened cream cheese. Mix slowly until the mixture becomes smooth and creamy with no large lumps.

Add chopped celery and green onions. Pour in lemon juice, then add salt and black pepper. Mix well until all ingredients are evenly combined. Taste and adjust seasoning if needed.

Place tortillas flat on a clean surface. If needed, warm them slightly to make them soft and easy to roll.

Spread an even layer of the chicken salad mixture over each tortilla. Leave a small border around the edges to prevent spilling.

Carefully roll each tortilla into a tight log. Place seam side down to keep it closed.

Wrap each roll in plastic wrap or cover and refrigerate for at least 1 hour. This helps the rolls firm up and hold shape.

Remove from refrigerator and unwrap. Use a sharp knife to slice into small pinwheels. Clean the knife between cuts for neat slices.

Arrange on a plate and serve chilled.