I need a formula to help with modeling an investment fund:

Let’s say an investor invests in a fund and cash flow from investments all goes to the investor until the investor gets a return of X%. Now that the investor realized return of X%, future cash flow will be split 50/50 with the fund manager until the manager receives 20% of total cash flow.

For example, using brute force I know that if the investor got $600K which got him to X%, then cash flow of $100k a year is split 50/50 ($50k to investor and $50k to manager), the manager would eventually receive $200k and the investor would have received $800k, and the manager’s share of total cash distributed to this point is 20%.

Is there a formula I can use to calculate what dollar amount the manager will receive by plugging in the variables of cash received by the investor, the % of cash split and the managers target total to be received (20%)?

I'm in for this one.

I can't even understand the question, so I can't wait to see the answer.

Not a single formula, but an algorithm can be made which could be translated into a spreadsheet.  You will have the following variables:
A - Initial investment amount (used to calculate all returns for the year)

B - Initial return % for investor (this % x A will be initial cash which all flows to the investor, per your example)

C - Target % payment to manager.

D - Actual cash flow to be divided between investor and manager.

E - Investor's share of cash flow ($)

F - Manager's share of cash flow ($)

G - Manager's targets payment (= C * A)

A x B = R [reserved cash flow to investor]
F=0, G = C*A
if (R>D) then E = D, else E=R [initial payment to investor - if there is not enough cash flow to exceed the investors starting target, then all cash flow goes to investor, otherwise investor gets the starting target)
D=D-E [initial amount to be distributed reduced by payment to investor]
If (D*.5)<G then F=D*.5, E=E+D*.5,  END**   [not enough cash flow to pay off manager's targeted payment %, so split remaining cash flow 50/50]
Else E=E+G, F=G, D=D-(G*2) [enough money available to pay manager up to his targeted percentage with 50/50 split]
F = F+ (D*C), E= E+ (D*(1-c))  [remaining money split between investor and manager based on the target % fee to the manager]

Final accounting:  F = amount to be paid to manager, E = amount to investor