No
NO.
As an ex Strike/Attack pilot with at least one tour in the Middle East under my belt + time with the MNPKF Lebanon in 1984 I understand a little about the area. Why have I said no?
1. Bombing will not solve this problem.
2. There are sufficient air assets already in the area.
3. To identify targets and be successful in this task we need effective intelligence and post attack info. At present, with no professional forces in that area we don't have that vital data.
4. The BBC today interviewed civilians in the towns and were told that much collateral damage was taking place.
5. I accept that the so-called Islamic State does pose a significant threat to the UK, but there are better ways to protect our island.
6. We do need ground forces in the area, but I cannot envisage the UK, France or the US committing to that.
7. The threat is not solely in Syria, but world wide.
I'm sure that you can think of many more reason why the UK should not bomb in Syria.