is_front_page is not working in my functions.php

add_action('init', 'save_landing_page_slider', 10, 2);

init is too early — if you look at the WordPress query overview on Codex, init is (as of writing) the second step, whereas is_ variables like $is_page (or WP_Query::$is_page) that are used by conditional tags like is_front_page() are only set in step 4, so instead of init, you should use a later hook like wp or template_redirect:

add_action( 'template_redirect', 'save_landing_page_slider' );

So in order for conditional tags to work properly, make sure to call them in the right hook or place.

Additionally, you should also understand when would is_front_page() return true, e.g. when your homepage is set to a static Page, and that you’re on the homepage.