I get a flu shot every year. As I understand it, the problem is that the 'flu shot makers' have to decide very far in advance which strains to protect against with the upcoming vaccine. Not sure but I seem to remember being told that the current one protects against 3 different strains, but could be wrong.
I had never gotten a pneumonia vaccine until this year when my doctor suggested it, so I went ahead and got the shot. As stated above he also told me that 2 will be required.
Why not just get both flu and pneumonia shots ? easy peasy.
If you want to get TRULY scared read up on the flu pandemic that hit during and just after WWI. Pay attention to the numbers of people who died from the flu compared to how many died during the war. I'll take all the flu shots I can get.