This Ruby script will bulk remove all Slack files older than 30 days. Just add your API token from https://api.slack.com/web#authentication into the token quotes at the top of the file.

slack_delete.rb

require 'net/http'
require 'json'
require 'uri'

@token = ''

def list_files(days)
  params = {
    token: @token,
    ts_to: (Time.now - days * 24 * 60 * 60).to_i,
    count: 1000
  }
  uri = URI.parse('https://slack.com/api/files.list')
  uri.query = URI.encode_www_form(params)

  response = Net::HTTP.get_response(uri)
  JSON.parse(response.body)['files']
end

def delete_files(file_ids)
  file_ids.each do |file_id|
    params = {
      token: @token,
      file: file_id
    }
    uri = URI.parse('https://slack.com/api/files.delete')
    uri.query = URI.encode_www_form(params)

    response = Net::HTTP.get_response(uri)
    body = JSON.parse(response.body)

    if body['ok']
      puts "#{file_id}: OK"
    else
      error = body['error']
      puts "#{file_id}: ERROR (#{error})"
    end

    # Sleep a little to ensure no rate limiting
    sleep 0.5
  end
end

files = list_files(days = 30)

puts 'Files that would be deleted:'
files.each do |file|
  created_datestamp = Time.at(file["created"])
  puts "#{created_datestamp}: #{file["title"]} (#{file["name"]})"
end

print 'Would you like to proceed? (y/N):'
proceed = gets.chomp

if proceed.downcase == 'y'
  file_ids = files.map { |f| f['id'] }
  delete_files(file_ids)
  puts 'Done!'
else
  puts 'User cancelled operation, exiting'
end