Great question! I would say, that it would be ok to, on occasion, to share your prayers on your other social media profiles.
The first thing that comes to mind is Matthew 6:6 where the Christ tells us to pray in secret. Now, this, of course, does not apply to ALL prayer, but is really aimed at those who use public prayer as a kind of attention grabbing gimmick. – I get the feeling that’s not what you’re after.
The question would you would want to ask is why you would want to post it on Facebook? Are you wanting to lead others to pray with you? If so, then I would probably post something that says explains that you’re here to help others pray and that you have some prayers that you say everyday and would like to share if anyone is interested.
Some people start specific pages for things like that so that people can subscribe to those types of things. Just an idea.
So, my general answer would be yes, go ahead and post a link to your prayer on Facebook.
Hope this answers