Thermal noise for hand calculation is most simply expressed as a drain current noise
Idn=4 k T Γ g_ms
where g_ms is the source transconductance and Γ a factor smoothly varying from 1/2 in weak inversion to 2/3 in strong inversion. It is valid for all regions of operation.
As of flicker that's a much stickier matter since modern models use very complex equations to describe partially correlated components. For hand calculation a simple enough equation would be
Vgn = Kf / (Cox W L ) 1/f
the frequency exponent might deviate from unity by quite a bit and Kf includes a lot of complexity: including dependence on operating point, temperature, and technology.
You can get a good idea from Arnaud's "Consistent Noise Models for Analysis and Design
of CMOS Circuits" IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS , VOL. 51, NO. 10, OCTOBER 2004