Sorry, but I did not find there the answer to my question. There were no experimental data for the velocity of climbing dislocation as function of the applied stress.
Dislocation climb is difficult to isolate because it is always mixed with glide... To my knowledge such measurements been done in HCP metals deformed along their c-axis (Edelin,G., and Poirier, J. P., 1973, Phil. Mag., 28, 1203, 1211.; LeHazif,R., Edelin,G., and Dupouy, J.-M., 1972, Metall. Trans., 4, 1274; Le Hazif R, Antolin J, Dupouy JM. Trans JIM 1968;9(Suppl.):247.) and in quasicrystals (F. Mompiou, D. Caillard / Acta Materialia 56 (2008) 2262–2271; F. Mompiou, D. Caillard / Materials Science and Engineering A 483–484 (2008) 143–147). The climb velocity can be fairly high provided stress and temperature are high enough.