Rice and corn flour/starch are frequently used in the manufacture of gluten-free products, which are usually characterized by high starch content, low fiber content, poor texture, insufficient volume, short shelf life, fast staling, and easy crumbling. The objective of this study was to use amaranth, quinoa, and chia flours, separately or in combination, and corn starch in different ratios as an alternative to wheat/rice flours. Furthermore, several hydrocolloids (methylcellulose, carboxymethylcellulose, xanthan gum, and guar gum) were added at different levels (2, 3, and 4%) to the precited flours in order to improve the technological properties of gluten-free bread, enhance its nutritive value, and avoid the negative effects caused by the ingestion of gluten for coeliacs. The increase in pseudocereal flours’ ratios produced dark dough and resulted in a decrease in specific volume and an increase in moisture content and crumb texture hardness in all bread formulations (except in quinoa breads). The increase in hydrocolloids’ levels contributed to an increase in the moisture content, specific volume, L values of crumb color, and hardness of all breads. The formulations prepared with the lowest ratio of pseudocereal flours (10%) at the highest hydrocolloid concentration (4%) produced better quality bread than the control in terms of acceptability. Among the pseudocereal-containing breads, quinoa breads had the best specific volume and crumb hardness, followed by chia, mixture, and amaranth breads. The formulations containing natural hydrocolloids combined with amaranth, quinoa, and chia flours could be interesting to produce “better-quality and healthier” bread for coeliacs.