AWS and Amazon e-commerce are vastly different services, yet Walmart refuses to use AWS because Amazon is also their largest competitor. In fact, Walmart built themselves an entire private cloud to avoid using AWS.
So OP actually raises a very good question: why does Netflix use AWS when Walmart does not?
The decision to build a private cloud sets back other priorities, like competing with Amazon on Grocery. It may, or may not, pay off for Walmart. If Walmart did store their data in Amazon's cloud, it is possible Amazon could use that information (sales, prices, etc) to more efficiently compete.
Conversely, if Netflix built out their own cloud, it could have come at the expense of delivering more content, which could risk unseat their position as the leader of streaming space.
Netflix stores their data on AWS (and probably spends more money than Walmart on it). Amazon could use that money to improve Amazon Prime Video (which competes directly with Netflix).
Because AWS is a huge profit center for Amazon, they are able to invest those profits into reducing prices on the retail side of their business - amazon.com. Netflix doesn't compete with Amazon's retail business, Walmart most certainly does.
Not really part of the same company. AWS is a subsidiary, and is run as a separate company. To them, Amazon is just one of their biggest customers — and not even THE biggest customer.
I think you're misinterpreting what OP is inquiring.
Amazon is the company. The company offers AWS and Amazon Prime Video (I am assuming you mean Amazon Prime Video rather than the e-commerce side of the business). Ergo, providing AWS enriches Amazon. Assuming funding within the company is fungible, Netflix is indirectly helping Amazon Prime Video.
OPs question is: Let's assume Netflix takes this as the antecedent- why do they still choose to indirectly enrich Amazon Prime Video, their competitor?
So OP actually raises a very good question: why does Netflix use AWS when Walmart does not?