Here's the dictionary entry I got, and it seems to fit the context: http://jisho.org/words?jap=%E3%81%8F%E3%82%89%E3%81%84&eng=&dict=edict&common=on

I think Mr Certainly is right. In this sentence, くらい　mean "same level". Truely white thing is dazzling, isn't it? ex) When we see the pure white paper or shining white snow. Her skin's beauty is same level as shining pure white. (when we see shining thing, we feel dazzling. So, he/her feel dazzling = her skin is shining) This sentence want to explaine her skin is very beatiful.Not rough. Japanese skin is yellow. But it not just yellow.We have various tone. And we think more white is more beautiful. In Japan, as the old proverb says " White color sikin covers 7flaw" 色白は七難隠す（いろじろは　しちなん　かくす）(irojiro ha sitinan kakusu) (The number "7" don't have special mean.It just emphasis) Well, we know other color skin is beatiful as white one. But even now, Japanese have admiration for white skin. So many whitening cosmetics sale in Japan.

but, くらい, generally means 'around' or 'about'. Given the sentence structure, the best interpreted sentence would be: Skin that's almost dazzlingly white and smooth like milk. 肌、まぶしいくらい、白い、なめらか、で、ミルクみたい <skin><bright enough><white><smooth><and><like milk> here the "kurai" is best converted to "almost" or "nearly". Also, みたい if you're not familiar with it, translates to 'like', but not 'the same' which is 同じ [おなじ].