Tadpole galaxies, with a bright peripheral clump on a faint tail, are morphological types unusual in the nearby universe but very common early on. Low mass local tadpoles were identified and studied photometrically in a previous work, which we complete here analyzing their chemical and dynamical properties. We measure Hα velocity curves of seven local tadpoles, representing 50% of the initial sample. Five of them show evidence for rotation (~70%), and a sixth target hints at it. Often the center of rotation is spatially offset with respect to the tadpole head (three out of five cases). The size and velocity dispersion of the heads are typical of giant H II regions, and three of them yield dynamical masses in fair agreement with their stellar masses as inferred from photometry. In four cases the velocity dispersion at the head is reduced with respect to its immediate surroundings. The oxygen metallicity estimated from [N II] λ6583/Hα often shows significant spatial variations across the galaxies (~0.5 dex), being smallest at the head and larger elsewhere. The resulting chemical abundance gradients are opposite to the ones observed in local spirals, but agrees with disk galaxies at high redshift. We interpret the metallicity variation as a sign of external gas accretion (cold-flows) onto the head of the tadpole. The galaxies are low-metallicity outliers of the mass-metallicity relationship. In particular, two of the tadpole heads are extremely metal poor, with a metallicity smaller than a tenth of the solar value. These two targets are also very young (ages smaller than 5 Myr). All these results combined are consistent with the local tadpole galaxies being disks in early stages of assembling, with their star formation sustained by accretion of external metal-poor gas.