Yes, it is perfectly fine for Christians to become wealthy, and there is nothing in the Bible that forbids Christians from gaining large amounts of money. The problem is that the love of money is the root of all sorts of evil (1 Tim. 6:10). Jesus said that you cannot serve both money and God at the same time: “No one can serve two masters; for either he will hate the one and love the other, or he will hold to one and despise the other. You cannot serve God and mammon (wealth),” (Matt. 6:24). Jesus is not saying that it is sinful to be rich. Jesus is telling us that the problem is when Christians start putting their faith, hope, and security in their money (and it becomes their master) rather than God. At this point, they become idolaters and fail to serve the true God.
Also, if a Christian is blessed by God to have large amounts of wealth, then he or she should use it for furthering the gospel. Therefore, wealthy Christians, just like poor Christians, should tithe to the church to aid it in expanding the gospel of Christ. Consider the parable that Jesus gave concerning the use of money in Luke 19:11-27. In it the person who was punished was the one who did not use the money given to him by his master in a manner profitable to the master, and he was condemned. So, when someone is given something by God, he is to use it for God’s glory. This includes money.