There is definitely a "shortage" - the inverted comma's are based on the fact that it may or may not be a shortage. I know that sounds odd, but the fact is that:
(a) even in developed nations, many people who can or should have the flue vaccine do not take it up (in my area, for example, take up by those entitled to it under the NHS is less that 70%)
(b) all countries across the globe have increased their orders for the vaccine massively.
Flu vaccine orders for the winter season are usually placed in January - March, so that the companies producing the vaccine can set in place the capacity to meet the orders. However, that capacity is impacted upon by two things - the shelf life of the flu vaccine is at most nine months, so it is impossible to stockpile, and the need to manufacture the right "viral mix" which means that you can't start manufacturing it until you know what the most likely strains of flu that winter are going to be.
My understanding is that most companies producing the vaccine have increased production, but that some are only able to produce about 20% more than normal. If there is a higher demand / take-up, that will lead to shortages. Although it has not been explicitly stated, I assume that is why the government, having initially said that they would vaccinate everyone over 50, has now downgraded that offer to "everyone over 50, later in the year, if there are supplies left".