The guidance in the UK is that it is fine to have the flu jab if you have any sort of cold, but only if you do not have a fever.
However, many doctors avoid administering the flu vaccine in these situations, asking patients to return after they have made a full recovery.
Vaccines challenge the body's immune system, putting it under stress. My opinion is that, if you choose to have the flu jab, it is better done when you are well, rather than when fighting an infection.
Rarely, symptoms of flu can arise after the flu jab and this could make it seem that your head cold has become worse, or that you take longer to recover.
Waiting another week would probably be advisable.