The wrong arguments are being made here. Yes, you have highlight the privilege he got from his family and ability to turn that into a success.
However, the critique builds out of that in multiple directions.
1. He's built a company on the backs of cheap and abused labour.
2. He's benefited from state backed intervention to make Amazon what it is today.
3. The "entrepreneur" myth has been used by governments to tear down unions, workers rights, social safety nets in the name of "everyone can be self-made if you get the state out of the way".
4. Governments/politics use Bezos/Amazon et al. to perpetuate the "bootstraps" ideology.
I don't care if Bezos got 250k from his family, what I care about and what I think others should as well, is how that success is sold to people in terms of labour, the political ideology of entrepreneurship and the dismantling of the social state. Bezos feeds into that and like many out of touch rich people, thinks philanthropy is the answer to social safety nets and the woes of the state and thus does not challenge how his "story" is used to influence politics.
If Bezos got 250k from his parents, made amazon what it is today, yet didn't try to bust unions, pay poverty wages, dis-endorse philanthropy, and fought back against his "story" being held up as an example that "everyone else just doesn't try as hard as Bezos and thats why you're poor", no one would give a flying feck. The argument should move beyond "250K and he's self made" to how their success also feeds into societal failures.