Only God knows your uncle's heart, and whether or not he is sincere when he says he is a Christian. The Bible warns us against judging others, for only God knows their hearts, and only He knows their true spiritual state. The Bible warns, "Do not judge, or you too will be judged" (Matthew 7:1).
However, if your uncle is a Christian, he is an inconsistent one - because what he is doing is wrong in God's eyes (as well as the eyes of the government). The Bible says, "Give everyone what you owe him: If you owe taxes, pay taxes; if revenue, then revenue" (Romans 13:7). When Jesus was asked on one occasion if it was right to pay taxes to the Roman authorities, He replied, "Give to Caesar what is Caesar's, and to God what is God's" (Matthew 22:21). Cheating on our taxes is a form of stealing, because it involves taking something that isn't rightfully yours.
The real issue, however, is why your uncle does this. Is it just to be clever and "outsmart the government"? I doubt it. Very possibly your uncle has put money at the center of his life instead of God - and that is a dangerous step. Jesus warned, "You cannot serve both God and Money" (Luke 16:13).
Pray for your uncle, and ask God to help him face his need to commit his life to Christ without reserve. And make sure of your own commitment to Christ as well, for He alone gives us a solid foundation for living.
Follow the Steps to Peace online to learn about Jesus or recommit your life to Him.