Here are three easy way to embed Instagram videos with nothing more than a link:
Embed.ly: This website is compatible with a variety of different media formats, able to embed code from dynamic pages. By default, the video will be 500 px by 500 px, but simply play around in the source code allows anyone to change the height and width to their desired square dimensions.
Embed Instagram: This service is helpful because it presents multiple sizing and format options, including the option to designate Flash or HTML 5, before generating embed code based on those selections.
Video for Everybody Generator: For those who like to see the code, this site fits the bill. The layout provides a lot more fields including a title field and a custom size field for height and width. The video will also be more accessible if a title is entered, because ALT text will be baked into the code.