We present a single-handed and eyes-free Japanese kana text input system on touch screens of mobile devices. We first conducted preliminary experiments to investigate the accuracy with which subjects could single-handedly point to and flick without using their eyes. We found from the results that users can point at a screen that was divided into 2 x 2 with 100% accuracy and that users can flick at a 2 x 2 grid without using their eyes with 96.1% accuracy using our algorithm for flick recognition. The system used kana letter input based on two-stroke input with three keys to enable accurate eyes-free typing. First, users flick for consonant input, and then similarly flick for vowel input. We conducted a long-term user study to measure basic text entry speed and error rate performance under eyes-free conditions, and readability of transcribed phrases. As a result, the mean text entry speed was 51.2 characters per minute (cpm) in the 10th session of the user study and the mean error rate was 0.6% of all characters. The mean text entry speed was 33.9 cpm in the 11th session, which was conducted under totally eyes-free conditions and the mean error rate was 4.8% of all characters. We not only measured cpm and error rate, but also measured error rate of reading, which we devised as a novel metric to measure how accurately users can read transcribed phrases. The mean error rate of reading in the 11th session was 5.7% of all phrases.