Regional accents of the same language affect not only how words are pronounced (i.e., phonetic content), but also impact prosodic aspects of speech such as speaking rate and intonation. This paper investigates a novel flow-based approach to accent conversion using normalizing flows. The proposed approach revolves around three steps: remapping the phonetic conditioning, to better match the target accent, warping the duration of the converted speech, to better suit the target phonemes, and an attention mechanism that implicitly aligns source and target speech sequences. The proposed remap-warp-attend system enables adaptation of both phonetic and prosodic aspects of speech while allowing for source and converted speech signals to be of different lengths. Objective and subjective evaluations show that the proposed approach significantly outperforms a competitive CopyCat baseline model in terms of similarity to the target accent, naturalness and intelligibility.