it usually takes at least 2 to 4 weeks for the flu shot to be effective. also, younger kids need to take 2 shots (at least 1 month apart) if it's the 1st time they take the flu shot.
don't take the flu shot if u're having fever or allergic to eggs.
that's not very common .... but my kid also got his first flu when he's almost 5 months old, and my 99 also worried he might be getting pneumonia but he ended up ok in about 2 weeks.
i also have a friend whose newborn (less than 1 month old) caught a flu (from her older kid) and needed to take antibiotics.