WCF Chapter 21, Of Religious Worship and the Sabbath, devotes significant attention to prayer, affirming that prayer with thanksgiving is one part of the natural worship God requires of all people, and is made acceptable to him through the name of the Son by the help of the Spirit. That framing is behind the whole passage: prayer is not a technique we master, it is a gift of access we have been granted through Christ and sustained in by the Spirit. The confession also affirms that prayer is to be offered with understanding, reverence, humility, fervency, faith, love, and perseverance, and that even corporate intercession for others is an expected part of the church's life.
WCF Chapter 26, Of the Communion of Saints, illuminates Paul's mutual prayer request. The confession affirms that saints are to maintain a holy fellowship in the worship of God, and in performing such offices as tend to their mutual good, both in the inward and outward man. Praying for one another across distance, as Paul does here, carrying each other to the throne of grace when you cannot be in the same room, is not a warm sentiment. It is what the communion of saints actually looks like in practice.