It may be the case that the Roman benefit that came closest to the modern concept of lawful privileges is that of Roman citizenship. In this incident involving Paul and the Roman tribune we are told about two levels of citizenship, one that came with birth, which Paul had, and one that could be purchased, which the tribune had. Of course, Roman citizenship did not exempt a person from trial at law, but it did protect him from cruel means of obtaining evidence. So Paul was prepared to use this privilege at times, and in addition, he had other privileges that he was also willing to use.
While it is not possible to comment on all the features of his privileges, there are several lessons that we can deduce from the fact that Paul possessed them. First, they were given to Paul in divine providence and he accepted that they were his to use. Paul was prepared to use all his privileges in providence, and for example in his speech earlier given to the mob in the temple he had made use of the status that he had as a former student of Gamaliel. When he referred to Gamaliel, it is similar to how a person today who has attended a top university, and did well there, could use that detail to draw attention to Christ.
Second, Paul used his privileges for the benefit of the churches at times. We have already seen that when he was in Philippi he mentioned his Roman citizenship to the authorities. Yet he did not mention it until after he had been beaten, which suggests that he did not refer to it for his own benefit (Acts 16:37). So it is likely that he mentioned it in order to provide some civic protection for the new church in Philippi after he had left the city. Paul used his privileges to express brotherly love.
Third, Paul taught Christians that they should pray for the government to rule justly and to provide a peaceful environment. There was the possibility here of great injustice taking place. Of course, there were occasions when it was not possible to avoid the injustice. Perhaps Paul discerned that the Roman tribune was intent on doing things according to the law. Whether or not that was the case, Christians should be concerned with matters of injustice and protest when it is happening. In the nineteenth century, many Christians were involved in ensuring that improvements were made to government policy concerning justice for those then under-privileged. And there are numerous example of injustice taking place today about which Christians should speak out.
Fourth, Paul's actions here inform us that there is no necessity for Christian to accept excruciating punishment if it can be avoided. Sometimes the impression can be given that a Christian should meekly accept all that is thrown at him. There is no requirement on a Christian that he bow to undeserved punishment.
No doubt, there are many other aspects of how a Christian should use the status he or she has in society. What it does mean is that some will have opportunities that others don't have. And if they have them, they should use them in a God-glorifying way.