How does uniswap creator take profit?
Uniswap itself made $11 million in their Series A funding round. (See here.) I believe they currently use this as their source of funds for operating and development.
However, the Uniswap contracts - at least in v2, I'm assuming also for v3 - do have a mechanism to take a fee from each trade.
In the Whitepaper, section 2.4 Protocol Fee:
Uniswap v2 includes a 0.05% protocol fee that can be turned on and
off. If turned on, this fee would be sent to a feeTo address specified
in the factory contract
This protocol fee would go to the treasury (creator). It would reduce the fee paid to the LPs from 0.3% to 0.25%. I believe this is currently turned off, with a view to turning it on in future.
(See: How is uniswap/sushiswap distributing their fees? for a discussion of the actual code.)
So how could you make profit if you created a DEX/AMM?
Turn on the per-swap protocol fee. Another option might be to include adding a one-time fee for the creation of a new trading pair/pool.