What exactly do you mean by "all cookies related to current tab"?
Any resource loaded over the network could be associated with a cookie. If you just want to get the cookies for all frames within the tab, then use the chrome.webNavigation.getAllFrames method to get a list of URLs associated with a tab. Here's a very naive method of getting all cookies.
chrome.tabs.query({
    currentWindow: true,
    active: true
}, function(tabs) {
    chrome.webNavigation.getAllFrames({
        tabId: tabs[0].id
    }, function(details) {
        // Get unique list of URLs
        var urls = details.reduce(function(urls, frame) {
            if (urls.indexOf(frame.url) === -1)
                urls.push(frame.url);
            return urls;
        }, []);
        // Get all cookies
        var index = 0;
        var cookies = [];
        urls.forEach(function(url) {
            chrome.cookies.getAll({
                url: url
            }, function(additionalCookies) {
                cookies = cookies.concat(additionalCookies);
                if (++index === urls.length) {
                    // Collected all cookies!
                    // TODO: Use cookies.
                    // Note: The array may contain duplicate cookies!
                }
            }); // chrome.cookies.getAll
        }); // urls.forEach
    }); // chrome.webNavigation.getAllFrames
}); // chrome.tabs.query
The previous method is naive, because the resulting array of cookies might contain duplicate entries (e.g. if the page contains http://example.com and http://example.com/index.htm, then you'll get two entries for a cookie on .example.com).
There are many ways to filter duplicates in a JavaScript array, you can see some methods in this question.
If you want to literally get all cookies associated with a tab, then you need to collect them using the chrome.webRequest API. Use the webRequest events to detect network requests and the Cookie request header and Set-Cookie and Set-Cookie2 response headers. You have to manually parse the cookie though.
If you want to quickly see all cookies associated with a tab (frames only, like the first method), you can also open the developer tools and look at Resources -> Cookies).
 (image source: https://developers.google.com/chrome-developer-tools/docs/resources)
(image source: https://developers.google.com/chrome-developer-tools/docs/resources)