I thought you wanted combined flashing and dimming? If so, as I said before, you'd need to lift the Enable pins of the L293D and feed in the PWM signals.
Do you have a spare unpopulated PCB? If so, assemble it with two CMOS 555 chips, no timing resistors and no L293D. You'll need to add jumpers on the back of the board to tie the CMOS 555 RST pins high. You can also omit the regulator and tap 5V from your assembled board. You'll also need two pots and four diodes, preferably low leakage Schottky, but ordinary 1N4148 will do at a pinch Take a pot and solder the steering diodes direct to its end tags, with the common leads (one A ,one K) twisted together in mid-air. Wire from the pot wiper and from the common leads of the diodes to the active pads of the timing resistor footprint. Repeat for the other 555. If when you test it you find the brightness increases anticlockwise, swap the wires to the pot.
Try 100K pots and 100nF timing caps - that should give you a PWM of around 120Hz.
Wire the PWM outputs (Vd and Vg at the unpopulated L293D footprint) to the enable pins you lifted of the L293D on the original board and you should be good to go. Its only 4 wires between the boards + 4 to the off-board pots so it shouldn't be too ugly.
If you are good with an Xacto knife you could even isolate pins 1 and 9 without lifting them, reinforcing the remainder of the track past pin 1 with a piece of wire, then drill extra holes next to them for the PWM wires. Lead the PWM wire through the new hole and solder to the pin pad, or better - use press-fit PCB pins, jumper to the LM293D pin pad, solder the wire on top-side and lock the PCB pin in place with a small drop of epoxy applied with a toothpick.
If you wanted to add a non-flashing mode, you'd need to override the outputs from the existing 555 chips to the L293D. You could simply ground Reset, to force the output low or Trigger+Threshold to force the output high, but that's a lot of extra wires and switches so it would probably be better to redesign the whole board.
You soon reach a point where if you've got any programming skills at all, its better to use a MCU - e.g. an ATmega 328P programmed with an Arduino bootloader, as then you can do stuff like sequential mode selection with a single switch, or making one pot (or better, a panel mount quadrature encoder) adjust several different settings depending on what you selected with the mode switch.