...i am mid way through a project...
What does that mean?
I'd work on one thing at a time.
1. Get the LEDs working and "simulate" the petal action with other LEDs. You can hard-code the "fake" clock-time data, and make it run fast so that you don't have to run it for 12 hours to test it.
2. Hook-up and program the real time clock. Get that working with LEDs.
3. Add the petals and the petal-power. Test the petals manually first by connecting power with no microcontroller control.
I'm not sure what the 74HC595 is for... Maybe to get more outputs? You'll need inputs from the clock ship, and you'll need outputs for the LEDs and the flexinol.
the petals will be electrically heated so the petal curls, and then the current is switched off so it uncurls (7.5sec to curl, 7.5sec to relax). while the petal does that the LED for that petal will stay shining on it.
If the LED is always on when the flexinol is active, they can share output pins. But, they might have to be powered separately.
so thats my idea. Flexinol is essentially an ohmic resistor and needs 0.4A to curl up in 1 second, so i expect i will need around 0.2A running though the flexinol...
The Arduino can't directly put-out that much current, so you'll have to boost it. Probably with one transistor or MOSFET for each petal.
And, what does that mean? 0.4A to curl it and 0.2A to hold it curled???? If you need to reduce/control the output current or voltage, you can use the PWM output pins.