Is CiviCRM a 'master database' / 'master system'?
Yes, CiviCRM would be a great match for what you're describing. CiviCRM is a central 'master' information hub that has quite a bit of reach out of the box:


membership data (What Is CiviMember? and the following sections are a good start)
mass emails (which can be integrated with MailChimp via an
extension)
Paypal integration for membership payments, donations and
event sign ups (using Paypal Standard or Pro)
integration into your Wordpress CMS with tiered permissions determining who can see/do what


Using KashFlow for accounting, there may be a little bit of custom work involved for you (or a developer) to customize the CiviCRM CSV export for accounting information (looks like Kashflow has a good bit of CSV instructions on what is needed for their system; without diving into the particulars, hard to say if custom work would be needed).  The default CSV accounting batch export from CiviCRM has a large number of fields: it would be a matter of making sure your Kashflow-needed fields are in that export and potentially removing the unneeded ones.

Personal testimony: prior to using CiviCRM, our organization had a separate contact management system for each department, and none of the systems talked with each other (and manual comparisons between them often resulted in conflicting information).  We have benefited 100x fold from the time and energy put into learning and customizing CiviCRM.  We have one central place, integrated with our website, that keeps all our information current and accessible for staff. I'm so glad we made the choice to introduce CiviCRM into our administrative process.