Matthew 6: 5. And whenever you pray you should not be like the hypocrites that love to stand in the assemblies and on the corners of the marketplaces to pray that they be visible to the sons of men. And truly I say to you that they have received their reward. 6. But when you pray enter your inner room and close your door and pray to your Father who is in secret and your Father who sees in secret He will reward you in open. 7. And when you pray, you should not be chatterers like the pagans, for they hope that by many words they will be heard. 8. Therefore, do not imitate them for your Father knows what need you have before you ask Him.
While it is true that our prayers between us and YHWH are private, there is NOTHING wrong with praying with and for each other out loud or even posting it on Facebook. I don't see anywhere in the Bible that tells us we cannot post a public prayer here.
The bottom line is, Yeshua was not telling us we should never pray in public; He was attempting to tell people to not be like the hypocrites who desire to be heard in order to show how pious or religious they are!
1 Thessalonians 5:17 tells us to "pray without ceasing." If we are to pray continually this means we should pray anytime, including in public without any fear of what others think or do. The point is, YHWH is always watching, and He's the only one whose opinion matters.
Divine communication is not some "super spiritual" experience as postured by some, but about being humble and obedient: "For the worship that is pure and set apart before Elohim the Father, is this: to visit the fatherless and the widows in their affliction; and: that one keep himself unspotted from the world." (James 1:27).
Prayer is a dialogue with Heaven, not a monologue. Yeshua's teaching stands as the demarcation between relationship with YHWH rather than a religion about Him. Prayer is meant to establish and maintain an intimate relationship, and accountability between each individual and YHWH.
By all means, keep private your personal dialogues with God. But please don't insist that we cannot pray outloud with or for others. The idea is not to be "flashy" about it in order to cause others to think we have some special insights into God and the Bible that others don't.