You should use the afterRender callback the fullpage.js plugin offers.

afterRender()

This callback is fired just after the structure of the page is generated. This is the callback you want to use to initialize other plugins or fire any code which requires the document to be ready (as this plugin modifies the DOM to create the resulting structure).

You can take a look at a live example here or you can even find it in the examples folder of the fullpage.js download.

And you can easily see the source code its using:

$(document).ready(function () {

    $('#fullpage').fullpage({

        verticalCentered: true,

        sectionsColor: ['#1bbc9b', '#4BBFC3', '#7BAABE'],

        afterRender: function () {



            //playing the video

            $('video').get(0).play();

        }

    });

});

UPDATE

This is no longer necessary in fullpage.js > 2.6.6.
It will automatically play the video when accessing the section as far as it has the tag autoplay in it:

<video autoplay loop muted controls=false id=myVideo>

    <source src=imgs/flowers.mp4 type=video/mp4>

    <source src=imgs/flowers.webm type=video/webm>

</video>

In case you only want to play it on section load (not on page load) use data-autoplay.
More info at the documentation.