Can flour be used interchangeably with starch?

No, flour and starch are very different things.

Starch is a molecule consisting of a chain of glucose rings. It is one of the main ways plants store energy. In practice, it is extracted from many different grains and tubers such as potato, wheat, tapioca and corn.

Flour is a food ingredient made from milling a grain very finely, and frequently also removing the outer hull of the grain. If nothing else is specified, saying just "flour" denotes non-whole-grain wheat flour.

It so happens that starch is a molecule present in large amount in many flours. Wheat flour is about 90% starch, and rice flour is close to 100%. But it is still incorrect to assume interchangeability, for the same reason that "pan" and "iron" are not interchangeable words even when you are holding a pan made from 100% iron.

In the cases where starch is less than 100%, it is even worse to use the terms interchangeably, because the parts which are present in a smaller amount often determine the properties of the flour, making it act much differently than pure starch in the kitchen. For example, white wheat flour contains around 10% gluten, which allows you to make risen bread with it.

Update

As for interchangeable usage: There are a few corner cases, as Jolenealaska's comment point out. For example, there are applications where you only need the properties of pure starch, but you can substitute a flour which is not 100% starch, and the remaining ingredients won't get into the way. Thickening is one such application, another one is preventing dough from sticking. But in general, you cannot assume that starch can be substituted for flour or the other way round. You'd have to know how it works in your recipe so you can judge if the substitution is possible.

As for the word use, some starches don't need to be extracted by a special process, because the plant part in question already consists of starch and nothing else. They are produced by milling this plant part, and they are both a flour and a starch at the same time. The prevalent use of the word "starch" or "flour" is then a matter of cultural accident, and, as David Richerby notes, it can happen that different languages or dialects pick a different term, but this happens rarely. The terms are usually distinct and not ambiguous, especially for plants where you use both, such as wheat flour and wheat starch.

Appendix: nitty gritty details on the special case of corn

The corn flour case is a very complicated one. There you have many words whose meaning can overlap:

• corn starch is only the milled inner part of the kernel. It is a flour which is also a starch. It can be modified, and then it shouldn't be technically considered a flour any more.
• cornflour is the UK term for the milled inner part of the corn kernel, as David Richerby points out. However, in many countries the word (or its literal translation) is used for whole grain corn flour, which is yellow, and chemically has other ingredients than pure starch.
• the milled whole corn kernel is sometimes also called polenta.
• polenta also can be a word for corn semolina, which is also a milled kernel, but the particle size is larger than a flour.
• yet another meaning of polenta is a pap cooked from a milled whole kernel of either size (semolina or flour).
• the pap cooked from pure corn starch is never a polenta, it is a pudding or blanchmange. These words are also used when the pap is cooked from pure starch extracted from another plant.