General
First, a helper function. Given a word list, this returns a dictionary that maps the sorted letters in each word to the words that use all of those letter.
def make_anagram_dict(words):
    """Return dict mapping sorted letters -> [words w/ those letters]
        >>> (make_anagram_dict(["act", "cat", "dog", "god"]) ==
        ... {'dgo': ['dog', 'god'], 'act': ['act', 'cat']})
        True
    """
    out = {}
    for w in words:
        sorted_word = "".join(sorted(w))
        out.setdefault(sorted_word, []).append(w)
    return out
Then, our main function, which uses that to find the most common anagram.
def find_most_anagrams_from_wordlist(wordlist):
    """Given list of words, return the word with the most anagrams."""
    # START SOLUTION
    all_anagrams_dict = make_anagram_dict(wordlist)
    highest_num_anagrams = 0
    most_anagrams = None
    for w in wordlist:
        sorted_word = "".join(sorted(w))
        number_anagrams = len(all_anagrams_dict[sorted_word])
        if number_anagrams > highest_num_anagrams:
            highest_num_anagrams = number_anagrams
            most_anagrams = w
    return most_anagrams