Make anchor tag fill 100% height and width of parent flex element, whilst being vertically & horizontally centered

Don't be afraid, make anchor flexbox too:

a {
    display: flex;
    justify-content: center;
    align-items: center;
}

and you should add align-items: stretch to parent of anchor.


Remove align-items: center from .content .panel--link and make .content .panel--link a.link a flexbox too and align it vertically using:

display: flex;
justify-content: center;
align-items: center;

See demo below:

body {
  height: 800px;
}
.main {
  height: 100%;
}
.content {
  height: 100%;
  border: 20px solid #fff;
  display: flex;
  box-sizing: border-box;
}
.content .column {
  flex-direction: column;
  width: 33.33333%;
  background: #374550;
  display: flex;
}
.content .panel,
.content .panel--link {
  box-sizing: content-box;
  flex: 1;
  border: 3px solid #fff;
  padding: 0px;
  text-align: center;
}
.content .panel .logo,
.content .panel--link .logo {
  margin: 7.5% 0px 0% 0%;
  width: 80%;
}
.content .panel .blurb,
.content .panel--link .blurb {
  width: 80%;
  margin: 7.5% auto 0% auto;
}
.content .panel .blurb h1,
.content .panel--link .blurb h1 {
  text-decoration: none;
  color: rgba(255, 255, 255, 0.6);
  font-weight: lighter;
  line-height: 220%;
  font-size: 0.85rem;
  margin: 0px;
}
.content .panel .tel,
.content .panel--link .tel {
  margin: 7.5% auto 5% auto;
}
.content .panel .tel h2,
.content .panel--link .tel h2 {
  text-decoration: none;
  color: #fff;
  font-weight: 500;
  font-size: 1.2rem;
  margin: 0px;
}
.content .panel--link {
  display: flex;
  flex: 1;
  justify-content: center;
  /*align-items: center;*/
  text-align: center;
}
.content .panel--link a.link {
  text-decoration: none;
  color: #fff;
  text-transform: uppercase;
  font-weight: 600;
  font-size: 1rem;
  letter-spacing: 3px;
  flex: 1;
  display: flex;
  justify-content: center;
  align-items: center;
}
@media (max-width: 768px) {
  .content .column--two {
    order: -1;
  }
  .content .column--two .panel--two {
    order: -1;
  }
}
.content .column--two .panel--one {
  flex-grow: 1;
}
.content .column--two .panel--two {
  flex-grow: 2;
  background: #374550;
}
.content .column--two .panel--three {
  flex-grow: 1;
}
<main class="content">
  <div class="column column--one">

    <div class="panel--link panel--one">
      <a href="#" class="link">
                        Panel 1
                    </a>
    </div>

    <div class="panel--link panel--two">
      <a href="#" class="link">
                        Panel 2
                    </a>
    </div>
  </div>
  <div class="column column--two">
    <div class="panel--link panel--one">
      <a href="" class="link">
                        Panel 3
                    </a>
    </div>
    <div class="panel panel--two">

      <div class="blurb">
        <h1>Lorem ipsum dolor sit amet, consectetur adipiscing elit. Proin lectus orci, imperdiet ac auctor non, tristique eget augue. Curabitur quis gravida lorem, sed maximus purus. Nunc sit amet mollis turpis.</h1>
      </div>
      <div class="tel">
        <h2>123 456 789</h2>
      </div>
    </div>
    <div class="panel--link panel--three">
      <a href="#" class="link">
                        Panel 4
                    </a>
    </div>
  </div>
  <div class="column column--three">
    <div class="panel--link panel--one">
      <a href="#" class="link">
                        Panel 5
                    </a>
    </div>
    <div class="panel--link panel--two">
      <a href="#" class="link">
                        Panel 6
                    </a>
    </div>
  </div>
</main>