Try replacing the content of .htaccess (root) with the following code:

RewriteEngine On
RewriteBase /
RewriteRule ^index.php$ - [L]

# add a trailing slash to /wp-admin
RewriteRule ^([_0-9a-zA-Z-]+/)?wp-admin$ $1wp-admin/ [R=301,L]

RewriteCond %{REQUEST_FILENAME} -f [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^ - [L]
RewriteRule ^([_0-9a-zA-Z-]+/)?(wp-(content|admin|includes).*) $2 [L]
RewriteRule ^([_0-9a-zA-Z-]+/)?(.*.php)$ $2 [L]
RewriteRule . index.php [L]

Source: https://stackoverflow.com/questions/28518723/wordpress-multisite-subsite-wp-admin-err-too-many-redirects