Expressions used in Everyday Spoken English in Social and Professional contexts
To 'have the stomach for something' means to have the kind of personality that gives you the determination or the ability to do things which are unpleasant or dangerous. If you 'don't have the stomach for something' it means you don't feel as if you have the skills or ability to do something. Usually, these expressions are used in relation to tasks that are unpleasant or morally questionable. You are more likely to hear this used in an informal context. Similar in meaning to 'having courage' or 'being yellow-bellied'.
In informal contexts, the expression 'to have the stomach for' or 'to stomach' can refer to your tolerance for particular types of food, such as spicy, fatty etc.