I am primarily interested in their KD and control RNA-Seq, so I ended up writing a couple simple functions to retrieve the file IDs, given the experiment accession. Hope this might be helpful for someone.

import os
import requests

def get(resource,
        url='https://www.encodeproject.org/{}/?format=json',
        headers={'accept': 'application/json'}):
    return requests.get(url.format(resource), headers=headers).json()

def get_exp(exp_acc):
    def format(file):
        return [file['accession'], \
               file['paired_end'], \
               file['replicate']['biological_replicate_number']]

    response = get(os.path.join('experiments/', exp_acc))
    controls = set()
    for file in response['files']:
        if file['file_type'] == 'fastq':
            yield ['KD'] + format(file)
            controls |= set(file['replicate']['experiment']['possible_controls'])
    for ctrl in controls:
        response = get(ctrl)
        for file in response['files']:
            if file['file_type'] == 'fastq':
                yield ['Control'] + format(file)

from pprint import pprint
pprint(list(get_exp('ENCSR426UUG')))