To indirectly study the internal structure of giant clumps in main sequence galaxies at $z sim 1-3$, we target very turbulent and gas-rich local analogues from the DYNAMO sample with the Hubble Space Telescope, over a wavelength range of $sim 200-480$ nm. We present a catalog of 58 clumps identified in six DYNAMO galaxies, including the WFC3/UVIS F225W, F336W, and F467M photometry where the ($225-336$) and ($336-467$) colours are sensitive to extinction and stellar population age respectively. We measure the internal colour gradients of clumps themselves to study their age and extinction properties. We find a marked colour trend within individual clumps, where the resolved colour distributions show that clumps generally have bluer ($336-467$) colours (denoting very young ages) in their centers than at their edges, with little variation in the ($225-336$) colour associated with extinction. Furthermore, we find that clumps whose colours suggest they are older, are preferentially located closer toward the centers of their galaxies, and we find no young clumps at small galactocentric distances. Both results are consistent with simulations of high-redshift star forming systems that show clumps form via violent disk instability, and through dynamic processes migrate to the centers of their galaxies to contribute to bulge growth on timescales of a few 100 Myr, while continually forming stars in their centers. When we compare the DYNAMO clumps to those in these simulations, we find the best agreement with the long-lived clumps.