The response to that (to Ubiqiuitin’s last several posts) is that dying al kiddush Hashem can only take place by definition if a person can’t get away. If a person is not trying to avoid it, it’s no longer dying al Kiddush Hashem – it’s suicide.
So davening al Kiddush Hashem would mean davening to be in a situation in which one can’t avoid it.
The counter-argument to that is that davening is in itself trying to make it happen instead of avoiding it.
And the counter-argument to the counter-argument is that davening is different. Not running away when someone is trying to kill you is not being killed al kiddush Hashem since you are not being killed – you are killing yourself. Davening to have the opportunity to be killed al kiddush Hashem means that you are davening to be in a situation in which you can’t save yourself and you’re being killed will be a kiddush Hashem.
The counter-argument to the counter-argument of the counter-argument is that davening is not different.
I think both arguments (on this point) make sense. I agree with DY that we constantly face similar stiras in our Avodas Hashem. The main difference here though is that we are talking about davening. And we don’t generally daven for such things. And I think that is what bothering Ubiquitin and others (including myself). But I don’t think the other position is illogical – I’m just not sure it’s correct.