If your blog is important for you then it may not be recommended to do what you are intending to do.
Google supports cross domain canonical but probably it's not recommended in your situation. If you still need to use then the best approach would be to have original content on LinkedIn and in your website you can place canonical to LinkedIn as you got full content on your website. Learn more: https://webmasters.googleblog.com/2009/12/handling-legitimate-cross-domain.html
The way it appears, you would like to market your content.
If you are serious about producing quality content then just market your content on different platforms.
To market your content you may consider following:
- Share your content on social media platforms.
- LinkedIn: You can do a short post with a button to go to your blog.
- To have better authority, you may consider having occasional unique content in your LinkedIn profile.