How can the flip flop neglect clear when given output is given as feedback?
I suspect that you are getting burned by mixing CMOS and TTL. The output of a 74ALS00 is only guaranteed to produce a HIGH voltage of 3 volts. Add in a diode drop of 0.7 volts, and in theory the input to the 4013 could be as low as 2.3 volts. Since the minimum input high voltage for a 4013 at 5 volts is 3.5 volts, this would produce the failure to oscillate that you're seeing. As a matter of fact, the minimum high output voltage you need from the 74AL00 is ~4.2 volts, and that is not obviously in the cards.

What you should do is replace the last inverter in your delay chain with a CMOS chip, and put a 1k pullup resistor on its input. Failing that, simply putting a 1k pullup resistor on the output of the last delay inverter may (possibly) solve your problem. Also, make sure the pulldown resistor at the diode cathodes is large, something like 10k.