According to this article (the choice of article has no significance other than it came up first in my Google search):
Remington's 12-gauge 2 3/4-inch Premier Magnum turkey load has 1 1/2 ounces of shot and a 1260 fps muzzle velocity
Converting these figures to metric, $m_{\text{shot}} = 0.0425$ kg and $v_{\text{shot}} = 384$ m/sec, so the momentum of the shot is:
$$ p = m_{\text{shot}}v_{\text{shot}} = 16.3 \space \text{kg.m/s} $$
To conserve momentum your momentum would also change by the same amount, so:
$$ m_{\text{Luke}}v_{\text{Luke}} = m_{\text{shot}}v_{\text{shot}} = 16.3 $$
and if we divide $16.3$ by your mass of about $77$ kg we find your velocity to be:
$$ v_{\text{Luke}} = \frac{16.3}{77} = 0.21 \space \text{m/s} $$
Your question asked how far the chair would move, but there is no way to calculate this because it depends on the frictional losses as the chair rolls and I have no way to know this. The best I can do is give you the initial velocity of the chair ($0.21$ m/s). You'd have to try experimentally measuring the chair+you roll distance as a function of initial velocity to determine the distance.