Print consonant and vowels
Your code is a little confusing.  You're using names like currWord and passing a word to checkVowel, which is then checking for 'aeiou' etc.  I think of vowels as letters, so on the face of it you appear to be checking whole words against individual vowel letters, which probably shouldn't match.  That said, maybe the file is ordered such that it's actually only reading letters at a time.  Either way, your code is unclear.

As has been said in the comments, whilst you've technically used threads to perform the printing, it's unlikely that this is the strategy that was expected to solve the problem.  There are many approaches that you could take to solving the problem, one of which might be something like this:

start ConThread
start VowelThread

Open File
ForEach word in file
    ForEach letter in word
        if Vowel
            StoreLetter
            Set VowelFlag
        else
            StoreLetter
            Set ConFlag
        while ReadNextLetterFlag not set give up control
        clear ReadNextLetterFlag

Shutdown...


The vowel/Con threads then consist of something like:

While not shutdown
    While ConFlag not set give up control
    clear ConFlag
    Retrieve letter
    Output to console
    Set ReadNextLetterFlag


Giving up control of the running thread could be achieve using yield (although this isn't particularly efficient) and you may want to pair it with sleep.

For flags, you probably want to look at either atomic and/or volatile variables.