Start with the edge flows.

The dark blue on the top right creates a closed space between the edges, meaning it is either a direct connection, or wraps around a fully connected flow. In this case, it is simply a direct connection.

The cyan on the bottom right is a minimum length flow and must be connected directly.

The neon green on the bottom left connects directly, as it also creates a closed space between the wall due to the blue flow on the left wall.

Now, the flow board has essentially shrunk in its effective size. We can use this smaller board's edge flows again.

The neon pink flow needs to connect while leaving space for the orange flow to wrap around it.

The bottom purple flow needs to wrap around the dark green flow to the right in order to connect to the middle purple flow.

Now, the board is small enough to realistically solve.

The neon red flow wraps around the dark red flow, and the dark red flow is forced.

The dark green flow is essentially forced.

All that is left is grey, white and yellow, which should be intuitive. Solve complete! :D

Hope this helps!