Silent speech recognition (SSR) converts non-audio information such as articulatory movements into text. SSR has the potential to enable persons with laryngectomy to communicate through natural spoken expression. Current SSR systems have largely relied on speaker-dependent recognition models. The high degree of variability in articulatory patterns across different speakers has been a barrier for developing effective speaker-independent SSR approaches. Speaker-independent SSR approaches, however, are critical for reducing the amount of training data required from each speaker. In this paper, we investigate speaker-independent SSR from the movements of flesh points on tongue and lip with articulatory normalization methods that reduce the inter-speaker variation. To minimize the across-speaker physiological differences of the articulators, we propose Procrustes matching-based articulatory normalization by removing locational, rotational, and scaling differences. To further normalize the articulatory data, we apply feature-space maximum likelihood linear regression and i-vector. In this paper, we adopt a bidirectional long short term memory recurrent neural network (BLSTM) as an articulatory model to effectively model the articulatory movements with long-range articulatory history. A silent speech data set with flesh points was collected using an electromagnetic articulograph (EMA) from twelve healthy and two laryngectomized English speakers. Experimental results showed the effectiveness of our speaker-independent SSR approaches on healthy as well as laryngectomy speakers. In addition, BLSTM outperformed standard deep neural network. The best performance was obtained by BLSTM with all the three normalization approaches combined.