while (available() == 0) {
    delay(10)
}

Here you hope you've achieved non-blocking IO using the InputStream. You imagine that the data would be somehow "trickling in" on its own and you could just wait for it to become available so you can pick it up without blocking in the subsequent read() call.

This behavior isn't universal to any InputStream. In fact, it probably only works with a SocketInputStream and there it also has issues: when the remote end has closed the connection, it will keep returning 0 until you make another read call to observe that the socket is closed.

In other implementations of InputStream, available() will always return 0 unless the stream is buffered, in which case it will simply tell you how much is left in the buffer. When the buffer is empty, the input stream implementation won't try to fetch any more data from the underlying resource until you call read().

Therefore I'd suggest at least narrowing down the receiver of your function to SocketInputStream, but for full correctness you should use NIO code instead.

Finally, if you find that for your specific use case the available() loop does work as expected and read() never blocks, then you should drop withContext(IO) because it is implies two costly context switches (to a background thread and back) and its purpose is only to run blocking code off the GUI thread.

Your code seems ok from the coroutines point of view, nothing to improve. Just call the function from a coroutine builder: launch - if you want a concurrency or async - if you want parallelism. For example:

yourScope.launch {

    val inputStream = BufferedInputStream(FileInputStream("filename"))
    val result = inputStream.use {
        it.readData()
    }

    // use ByteArray result
}

Additional you can a little bit reduce your code replacing return@withContext buffer with buffer and moving withContext(Dispatchers.IO) out of the function's block:

suspend fun InputStream.readData(): ByteArray = withContext(Dispatchers.IO) {
    while (available() == 0) {
        delay(10)
    }
    val count = available()
    val buffer = ByteArray(count)
    read(buffer, 0, count)
    buffer
}

In addition the Marko's answer I'd like to point that the fact you cannot turn your blocking code into non-blocking one just by using coroutines doesn't mean you should not use coroutines whatsoever. It makes sense to use them in order to get other benefits:

1. It enables to keep sequential style for asynchronous code. If you have several steps to complete a whole task you don't need to use special reactive types and its combiners.
2. Provides a great way to scale task execution. In the case of multiple tasks you can execute them structurally in several contexts and and by different dispatchers.

Hope this helps to comprehend the whole picture.