Go get a flu shot. When we did it last time, I asked this exact question. And they said no, it won't make you anymore susceptible. It may not be as effective, but still... if it is somewhat effective, that is better than nothing.
Also, if you do end up getting it... they say that the flu shot lessens the effects of the flu.
Told me of a very healthy young woman who died of the flu. Things can go South very quickly.
In terms of flus shot, yes it takes ten days to two weeks to kick in. Also, many people get it too early, October, for example. Peak flu season is December to January and if u get it too early it is.not as effective now. That is per NYTimes piece.
Consider going to the doctor to get Tamiflu for the kids. It's very expensive, but it helps reduce the effects and duration of the flu. All three of my kids got the flu a year ago and I think Tamiflu helped. As for you, why not get the flu shot ASAP? There is no down side.
To pay close attention to those kids. I had a fever north of 103 and was coughing very hard, hacking up massive amounts of phlegm and choking on it. Coughed up tinges of blood. My doctor said I likely had the flu and told me if I ever had that severe a case to go to the hospital.
If your kids end up with pneumonia, it can get very serious very quickly.
And I’ll just speak for myself. Get a flu shot.