Can a gp rule out blood clots with blood pressure and listening to your chest?

No: But if pulse oximetry is "ok" and the history is unlikely, then additional testing may not be warranted.

Probably not: You didn't say where the blood clots might be. For blood clots in the legs a venous doppler (ultrasound) is usually ordered. For blood clots in the chest, the first test is usually a blood test called the d-dimer. Other tests can be ordered if the d-dimer is elevated. If the doctor feels your risk is very low, tests might not be needed.