We've built a tool for this use case. It's called Outclip -- https://checkoutclip.com. You'll need to install the Outclip chrome extension (click on 'get chrome extension' on the above webpage) and after that it's a couple of clicks to start a screen recording. After you stop recording, within a few moments you'll have a link (e.g. https://video.checkoutclip.com/-LDQ5TtL_yywYCgUNb6K) you can share with others or use in a bug report. People can click the link to view the video.

We don't support gif creation, to do that you can download the video file (.mp4) from Outclip and use a service like https:///cloudconvert.com to convert to gif.