To change the order of the accounts, go to Menu > Accounts. On the left side of the window that appears, you’ll see a list of the accounts that you have linked with eM Client.

If you want to change the order of these accounts, simply click on one of them. Then use the Up or Down buttons in the top toolbar to move the account in the desired direction. This changes the order of your accounts in the main Mail tab.
The location of the Local Folders and Archive cannot be changed.

IMPORTANT: Please note that changing the account order is not the same thing as setting an account as default. The default account is always the one marked by a star, not necessarily the first one on the list.