Is there unnecessary duplication for borrowing in this circular flow of income diagram? Here is a circular flow of income that I took from Krugman's macroenomics textbook.

We can see that when firms want to borrow they can go to the financial sector and borrow savings of national and foreign households. BUT, it seems like there is also another way for firms to borrow money: the factor market. Capital is a factor of production. And there are different kinds of capital, in our case we're interested in financial capital, specifically in financial capital that is basically a pile of money. And how can we, sort of, buy such financial capital? By borrowing it! So firms "buy" financial capital from households and then pay them interest (you can see that interest is paid to households from the diagram).

I don't get the purpose of this duplication. Why use financial sector for borrowing when we have the factor market? Or why use the factor market for borrowing when we have the financial sector? Is there some kind of important difference between them that makes both of them necessary in borrowing? Or did I make a mistake in my reasonings and firms can't get borrow money from the factor market? If yes, then why do households get paid interest from the factor market?
No because the financial markets do not provide firms with capital they provide them with funds to buy capital which is a difference. You can call those funds financial capital but it’s not capital in economic sense.

In common usage in English capital is often used as a synonym for money. For example in Oxford dictionary under the word capital the second entry is simply money (see here).

However, in economics capital, especially when we are talking about factor markets, is used in the following definition:

“The equipment and structures used to produce goods and services.”

The above definition is taken from Mankiw and Taylor (2014), Economics the 3rd edition. In different textbooks the exact wording may change but to my best knowledge no conventional textbook would include money as it’s definition.

Also generally money is not considered a factor of production in itself hence it’s a tautology that factor markets should provide only factors of production.

Moreover, generally financial markets are often considered quite distinct from other economic activity. In fact often you can hear economists speak of ‘real’ economy and financial markets separately. This is due to the classical dichotomy which makes sharp distinctions between real and monetary (nominal) variables. Factor markets are considered to be part of real economy, where real goods, services, and factors circulate, while financial markets are part of monetary sector which covers the circulation of money and other financial goods and services. 



In comment @user161005 asks additional question of why the arrow going to factor markets includes interest, since answer to this might be of interest (no pun intended) to other users who skip comments I put the answer also here:

In economics the income derived from labor is called wages, the income from land rent, and income derived from capital interest. 

The last often confuses students because many textbook models call the interest earn from capital $r$ instead of $i$ but this is because $i$ is already used widely in other macroeconomic models. 

The profit is what is left after the wages are paid to the labor, rent to landowners and interest to capital owners. Profit is considered to be the reward for entrepreneurship which can be considered as another factor of production. 

A good entry level explanation of this is provided in this FED St. Louis podcast that you can listen to (or read transcript to) here.