I've done a video in the past on how to use Lightroom's Publish Services to post photos directly from Lightroom to Instagram and Facebook. Unfortunately due to changes with the Facebook API this is going to be going away. You can read about the specific reasons on Adobe's website.
Now, the Publish Services is a very powerful tool for photographers and makes posting to social media sites very easy. I did not want to go back to exporting photos, transferring them to my phone, then uploading to the individual social media apps.
The "work around" I found is pretty simple, doesn't add too many steps, and hopefully it will stay around for a while.
The two things you need to start is an Adobe CC account and you need to have your Facebook page that you want to post to linked to your Instagram account that you want to post to.
Inside Lightroom, you're going to create a collection for your social media posts and make sure it is synced to Lightroom CC. Pick the photos that you want to post and add them to the collection. Once the photos are finished syncing open up the Lightroom CC app on your phone and go into the collection.
Select the photo that you want to post and click the share button at the top (box with the arrow). Choose the photo size and the phone will open up a sharing menu. In that sharing menu select "Copy to Instagram."
Once you click Copy to Instagram, Instagram will open and you will have the choice to add the photo to you story or to your feed. Pick where you want to post the photo.
If you choose feed the normal upload sequence will commence where you pick the cropping, filters, and you add your captions tags, and locations. On the page where you add your captions, as long as you have connected your Facebook account, you will also have the option to post the photo to Facebook (and Twitter and Tumblr) at the same time you post to Instagram. Make sure the button next to Facebook is selected (it will be blue) then press share.
Give it a few seconds and the photo along with the caption will be posted to both Instagram and Facebook.
Check out the video below to see the start to finish how to.