The average solar flux received in LEO is approximately the solar constant, or $1,361 \ \mathrm{W/m^2}$ at 1 astronomical unit (AU) from the Sun, though it can vary a bit since the solar irradiance received by an object is really function of distance from the Sun and not constant at all, since the Earth's distance isn't fixed at 1 AU. It works for us in this case though because the Earth's distance from the Sun does not vary too much throughout the year.
To understand where this number comes from, first we will evaluate the total power output from the surface of the Sun ($P_{sun}$) from the following equation,
$$P_{sun} = \sigma \ T^4 \ 4 \pi R_{sun}^{2} = 3.851 \cdot 10^{26} \ \mathrm{W}$$
where $\sigma$ is the Stefan-Boltzmann constant ($5.670374 \cdot 10^{-8}
\ \mathrm{W \ m^{-2}\ K^{-4}}$), $T$ is the temperature of the Sun ($5778 \ \mathrm{K}$), and $R_{Sun}$ is the radius of the Sun ($696,340 \ \mathrm{km}$). Be careful with units here.
Next, to determine power received per unit area at Earth's distance from the sun (or for your case in LEO), we divide $P_{Sun}$ by the area of a sphere with a radius equal to Earth's solar range ($r_{Earth}$) i.e.
$$\frac{P_{Sun}}{4 \ \pi \ r_{Earth}^2} = 1361 \ \mathrm{W \ m^{-2}}$$
where $r_{Earth}$ is approximately 150 million km (i.e. 1 astronomical unit).
This value can be used for your power system sizing - though of course you will need to take into account the cell conversion efficiency of your solar arrays to determine power generated for a given area!
