I don't have any side effects 3 days after getting first dose of covid vaccine. Does it mean that the vaccine is not working? ?

No, every one reacts differently to vaccines. Some people have a sore arm (or soreness at the site of the injection) for a day or a few hours. Some people feel sick, or they get side affects from the vaccine more sever then others.

I got the flu shot, I had a sore arm for a few hours. My grandmother got the flu shot and she was adamant that she got the flu from it.  

Probably not.  I've had a lot of vaccines, and the worst symptom I had is one day of discomfort at the injection site.

Its hard to say. Guessing your immune system is probably good. People sometimes think vitamins don't work. Its because they didn't have a vitamin deficiency.

i dont think so, you just got lucky

Not necessarily.  Everyone's different.  Some people will have a reaction to a vaccine some won't.  This is the same of any vaccine and not limited to the covid ones.

There are people that have a reaction to flu vaccines and some that don't.

No, it just means you didn't get any side effects.  

It's not uncommon to get side effects, but it also shouldn't mean that side effects entail that it's working. If You're not experiencing anything, You should be fine.