The quick-and-dirty one-liner is:
mylist = ["danny","florence","micheal","klrv","yrcv"]
mylist_no_vowel = [word for word in mylist if not any(character in 'aeiou' for character in word)]
Explanation
The second line uses a syntax called a list comprehension, which is a Python idiom for building a list (in this case, by filtering another list). The code is equivalent to:
mylist = ["danny","florence","micheal","klrv","yrcv"]
mylist_no_vowel = []
for word in mylist:
if not any(character in 'aeiou' for character in word):
mylist_no_vowel.append(word)
Translating, we start an empty list called mylist_no_vowel, then we iterate through each word in the original list mylist. For each word, we check if any of their characters is a vowel, using the any function. If that's not the case, we add the word to the mylist_no_vowel list.
Note that I changed your starting list variable name from list to mylist, since list is actually a reserved word in Python - you're overwriting the built-in list function by naming a variable like that!
list, it overrides the builtinlistfunction. :)