You are eligible to contribute to an HSA for any period that you are covered by a qualifying HDHP and not covered by "other coverage". The FSA is "other coverage", but assuming you can't request reimbursement from it now that you ended your employment, then you don't have "other coverage" as of August and can contribute to an HSA.
What I don't know is if the "last month" rule applies in your situation. You can definitely contribute 5/12ths of your annual maximum for the last 5 months of the year. The last month rule might allow you to contribute your entire annual maximum, but I don't know if it applies.
@dmertz will know the answer to that one.
Incidentally, your annual maximum for 2018 is $3450 if you are covered by a single HDHP, or $6900 if you are covered by a family HDHP, plus an additional $1000 catch up amount if you are 55 or over.