Deep learning has enabled significant advances in feedback-based channel coding, yet existing learned schemes remain fundamentally limited: they employ fixed block lengths, suffer degraded performance at high rates, and cannot fully exploit the adaptive potential of feedback. This paper introduces Deep Variable-Length Feedback (DeepVLF) coding, a flexible coding framework that dynamically adjusts transmission length via learned feedback. We propose two complementary architectures: DeepVLF-R, where termination is receiver-driven, and DeepVLF-T, where the transmitter controls termination. Both architectures leverage bit-group partitioning and transformer-based encoder-decoder networks to enable fine-grained rate adaptation in response to feedback. Evaluations over AWGN and 5G-NR fading channels demonstrate that DeepVLF substantially outperforms state-of-the-art learned feedback codes. It achieves the same block error rate with 20%-55% fewer channel uses and lowers error floors by orders of magnitude, particularly in high-rate regimes. Encoding dynamics analysis further reveals that the models autonomously learn a two-phase strategy analogous to classical Schalkwijk-Kailath coding: an initial information-carrying phase followed by a noise-cancellation refinement phase. This emergent behavior underscores the interpretability and information-theoretic alignment of the learned codes.