It all depends on how fast / reliable the sites serving the content are, and how fast your server is. Many high-traffic sites use a content delivery network (CDN, such as Akamai) to serve their static content, since CDNs have servers located in many areas and can usually receive content faster for the user.
My assumption is that these icons are hosted by many different providers, which means that the โuptimeโ of your site (as determined by the entire loading of content properly) will be the lowest common denominator of uptime for all sites that host your Images.
You also need to consider that since you do not control the sites that host these images, they can move / delete them at any time, and then they will be broken.
How often do you change images on your site? If this is not so common and you are concerned about operability / performance, I will probably try to serve them all from the host that you control, whether it be your own machine or something else.
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