No, it does not. You didn't actually look at the numbers. One of the worst years overall shows 115 for 0-4 and 528 for 5-17:
https://www.cdc.gov/flu/about/burden/2017-2018.htm
There are some years where the total is a little over a thousand, but most are well below.
Don't spread this bull.
This is false if you include the period during which COVID-19 has been around in “every year”, because COVID countermeasures also suppress the flu. Without COVID countermeasures, and without vaccination for most kids, COVID would kill far more than the flu normally does. Now, the COVID vaccine right now is more effective than the flu vaccine usually is (but that may be temporary if COVID is endemic and different variants proliferate), so with vaccines available to younger kids than now that might get evened out or reverse, but right now COVID is clearly far more deadly to kids.
I'm already bored to tears talking about this, though. The only point that I'm trying to make is that we have always accepted a certain level of mortal risk to people, including children. At some point, we are going to have to do that with Covid as well.
The bull that was clearly quoted? "Influenza kills thousands of people under 18 every year". The linked data does not say that at all.
You're being difficult just to be difficult here.