Python function to count syllables in a word
As a good practice to promote code reuse, the function should return a numeric result.  The print() should be done by the caller.

Constantly referring to is_previous_vowel is tedious. There are a couple of solutions you could use involving itertools. In particular, groupby() and zip_longest() could be useful.

Ultimately, the simplest solution is to use a regular expression to declare what you are looking for: one or more consecutive vowels ('[aeiouy]+'), but not an e at the end ('(?!e$)).

import re

def count_syllables(word):
    return len(
        re.findall('(?!e$)[aeiouy]+', word, re.I) +
        re.findall('^[^aeiouy]*e$', word, re.I)
    )