Conditional-flow text-to-speech (TTS) models can achieve high synthesis quality with relatively few sampling steps, but collapsing the remaining trajectory to a single update can still cause substantial quality degradation. We propose MixiSpeech, a progressive state distillation framework that converts a multi-step conditional-flow acoustic model into a one-step generator while preserving its architecture and speaker conditioning. Rather than training the one-step model directly, MixiSpeech progressively reduces the global sampling budget through a 10-4-2-1 curriculum, with each student trained to match local teacher-integration endpoints using a masked state-matching objective. We instantiate the framework on a 710-speaker Vietnamese Matcha-TTS model trained from scratch on PhoAudiobook. On 100 shared test text-speaker pairs, direct one-step inference substantially degrades synthesis quality, obtaining 1.6846 UTMOS22-Strong and 6.21% WER compared with 2.2923 and 4.65% for the 10-step teacher. In contrast, the distilled one-step model achieves 2.2678 UTMOS22-Strong, 4.63% WER, and 2.83% CER, recovering most of the quality lost at the one-step operating point while requiring only a single acoustic vector-field evaluation. End-to-end inference time decreases from 0.0662 s for the 10-step teacher to 0.0312 s for MixiSpeech, corresponding to a 2.12 measured speedup. These results show that progressive state distillation can make one-step conditional-flow TTS practical without relying on a large multi-step sampling budget. Project page: https://mixispeech.solanai.us/