For Dowex-50 we use step gradients, such as water then 4 M HCl. We make large pools, comprising several column volumes. We often load the amino acid in 0.5 column volumes of water, then use 1.5 column volumes of water as a wash. Then we use 2-3 column volumes of HCl. If an amino acid elutes slowly (and when there is a hydrophobic side-chain, it has in our hands), then the product still make show up in more than one pool. We take several pools, rotovap/vacuum, and check masses.
Dowex-50 is an old-school technique for purifying amino acids. Often people used water followed by 2 M ammonia , and I have used this many times myself in the past. Although I have seen people back the ammonia down to 0.5 M once or twice (presumably for sensitive side chains), I decided to avoid any possibility of its attacking the amino acid, and that is why I chose to elute with HCl. 4 M HCl is probably overkill, but people have used it before, so I just decided to try it. We only occasionally use TLC on amino acids, but Stahl's venerable TLC book gives five common solvents. 70:30 ethanol/water is one of them. There are both acidic and basic conditions.
We occasionally use Dowex-1 in the acetate form, but it does not always work in our hands for reasons that are not known to me. The idea is for the carboxylate group of the amino acid to displace an acetate ion on the resin. Acetate is less strongly bound to the resin than chloride; the conversion of the resin from the chloride form to the acetate form is lengthy but not difficult. If you need any references or protocols, just let me know.
This brings me to a question. Someone once asked me if I knew of any papers on the purification of amino acids by ion-exchange. I said that I did not, but that I could almost write one. Since that time my students and I worked out one additional method that is applicable when the side chain carries a charge. Would any journal or serial publication (by which I mean something like Methods in Enzymology) be interested in such a work?
Just FYI, there are some reviews (I have not read them in a while) of unsaturated amino acids that deals a little with isotope labeling:
Kaiser J et al., Org. Biomol. Chem. 2005 3:3435-3467. (a review which covers 2000-2005)
DOI: 10.1039/b001538p (a review which covers 1990-2000 IIRC)