To our knowledge, Jesus never spoke in tongues.
We have so little insight into his personal life, it is difficult to say anything definitive about his private practices. If he did speak in tongues for his own edification, no one was there to witness it. If some one did witness it, no biblical author was ever impressed by the Holy Spirit to record it. Although if someone had witnessed him doing so, I feel fairly certain it would have been recorded in light of Acts 2.
As far as his public ministry goes, we have no recorded incidence of Jesus ever speaking in tongues. We do have incidences of him speaking in Aramaic, but that was his native language, not the supernatural occurrence of speaking in tongues. Again, in light of Acts 2, had he spoken in tongues, I feel fairly certain one of the gospel authors would have recorded it. Something so seminal in the birth of the church would have surely had a precedent in the life of Christ recorded if there was one.
Regardless, I think the real issue implied by this question is that if Jesus never did, why should we? The answer is that regardless of what Jesus' experience was in this respect, at its beginning the church unanimously spoke in tongues, and the experience was promised to all that followed. For the disciples and those selected to be Apostles by Jesus, the clear choice of God was that every one of them spoke in tongues upon their baptism in the Spirit, even if Jesus never did.
So, the particular experience of Jesus in regard to speaking in tongues is not the controlling precedent for those who follow him. Instead, it is the experience of those who first followed Jesus which is the model for Christian experience. Jesus may have not spoken in tongues, but his followers did, and so can we!