If you want to run chromium-43.0.2357.132.sfs testing work is been the tahrpup.

for old puppy distro, i have uploaded chromium-37.0.2062.94.sfs flash version 17.0.0.188, i have test, lina-1.3 precise-5.7.1 slacko-5.5.0 slacko-5.7.0 maybe you need extra libs lib6+libstdc6-4.9.2.pet nspr_nss.pet see here the libs nspr_nss.txt
Note:Maybe to need upgrade in the last version the mozilla firefox.