The First Large Absorption Survey in H i (FLASH) is a large-area radio survey for neutral hydrogen in and around galaxies in the intermediate redshift range
$0.4\lt z\lt1.0$, using the 21-cm H i absorption line as a probe of cold neutral gas. The survey uses the ASKAP radio telescope and will cover 24,000 deg
$^2$ of sky over the next five years. FLASH breaks new ground in two ways – it is the first large H i absorption survey to be carried out without any optical preselection of targets, and we use an automated Bayesian line-finding tool to search through large datasets and assign a statistical significance to potential line detections. Two Pilot Surveys, covering around 3000 deg
$^2$ of sky, were carried out in 2019-22 to test and verify the strategy for the full FLASH survey. The processed data products from these Pilot Surveys (spectral-line cubes, continuum images, and catalogues) are public and available online. In this paper, we describe the FLASH spectral-line and continuum data products and discuss the quality of the H i spectra and the completeness of our automated line search. Finally, we present a set of 30 new H i absorption lines that were robustly detected in the Pilot Surveys, almost doubling the number of known H i absorption systems at
$0.4\lt z\lt1$. The detected lines span a wide range in H i optical depth, including three lines with a peak optical depth
$\tau\gt1$, and appear to be a mixture of intervening and associated systems. Interestingly, around two-thirds of the lines found in this untargeted sample are detected against sources with a peaked-spectrum radio continuum, which are only a minor (5–20%) fraction of the overall radio-source population. The detection rate for H i absorption lines in the Pilot Surveys (0.3 to 0.5 lines per 40 deg
$^2$ ASKAP field) is a factor of two below the expected value. One possible reason for this is the presence of a range of spectral-line artefacts in the Pilot Survey data that have now been mitigated and are not expected to recur in the full FLASH survey. A future paper in this series will discuss the host galaxies of the H i absorption systems identified here.