I believe it is wise and biblical to seek to be prepared for persecution. That's why I loved reading the Principles book. I believe it is good to pray for our hearts to be prepared for persecution be it mild or severe, that we may not deny His name when that time comes.
I also believe it is our duty to pray for the persecuted church around the world.
However, I do not believe it is wise nor biblical to pray for persecution or to focus that much attention on it, or to elevate the persecuted church above all other churches or Christians.
As has been stated on this thread, The Bible makes it clear that persecution is inevitable if we seek to truly live a godly life in Christ Jesus. I think a good prayer in light of that truth would be, "Lord, help me to live godly in Christ Jesus, and to prepare for inevitable persecution that comes with that."
A passage of Scripture that came to mind is 1Cor.7:17-24
"But as God has distributed to each one, as the Lord has called each one, so let him walk. And so I ordain in all the churches. 18 Was anyone called while circumcised? Let him not become uncircumcised. Was anyone called while uncircumcised? Let him not be circumcised. 19 Circumcision is nothing and uncircumcision is nothing, but keeping the commandments of God is what matters. 20 Let each one remain in the same calling in which he was called. 21 Were you called while a slave? Do not be concerned about it; but if you can be made free, rather use it. 22 For he who is called in the Lord while a slave is the Lord's freedman. Likewise he who is called while free is Christ's slave. 23 You were bought at a price; do not become slaves of men. 24 Brethren, let each one remain with God in that state in which he was called."
Verses 21 and 24 especially stand out to me here. God tells us in verse 21 that we are to take advantage of any opportunity we have to be outwardly free, so in light of that it wouldn't make sense to pray for persecution.
I'll post Matthew Henry's take on those two verses since I think he does a good job at breaking them down:
Verse 21
"Now," says the apostle, "art thou called being a servant? Care not for it. Be not over-solicitous about it. It is not inconsistent with thy duty, profession, or hopes, as a Christian. Yet, if thou mayest be made free, use it rather," v. 21. There are many conveniences in a state of freedom above that of servitude: a man has more power over himself, and more command of his time, and is not under the control of another lord; and therefore liberty is the more eligible state. But men's outward condition does neither hinder nor promote their acceptance with God. For he that is called being a servant is the Lord's freed-man””apeleutheros, as he that is called being free is the Lord's servant. Though he be not discharged from his master's service, he is freed from the dominion and vassalage of sin. Though he be not enslaved to Christ, yet he is bound to yield himself up wholly to his pleasure and service; and yet that service is perfect freedom. Note, Our comfort and happiness depend on what we are to Christ, not what we are in the world. The goodness of our outward condition does not discharge us from the duties of Christianity, nor the badness of it debar us from Christian privileges. He who is a slave may yet be a Christian freeman; he who is a freeman may yet be Christ's servant. He is bought with a price, and should not therefore be the servant of man.
Verse 24
"He sums up his advice: Let every man wherein he is called abide therein with God, v. 24. This is to be understood of the state wherein a man is converted to Christianity. No man should make his faith or religion an argument to break through any natural or civil obligations. He should quietly and comfortably abide in the condition in which he is; and this he may well do, when he may abide therein with God. Note, The special presence and favour of God are not limited to any outward condition or performance. He may enjoy it who is circumcised; and so may he who is uncircumcised. He who is bound may have it as well as he who is free. In this respect there is neither Greek nor Jew, circumcision nor uncircumcision, barbarian nor Scythian, bond nor free, Col. 3:11. The favour of God is not bound."