Continuing the discussion.
Cladistic analysis shows that there are the three groups I mentioned (dinosaurs, flying birds and flightless birds) but it does not tell us the time (sequence) relationship between these groups. In fact, it does not even tell us if there is any real phylogenetic ("evolutionary") relatedness between dinosaurs and birds at all. Those questions lie outside the realm of cladistic character analysis itself. They are assumptions that the cladist builds into the analysis.
The correct relationship between these three groups is the one that I have outlined:
Dinosaurs (eg. Tyrannosaurs) are not related to birds.
Primitive flying birds (eg. Dromaeosaurids) co-existed with dinosaurs.
Primitive secondarily flightless birds (eg. Oviraptors) came after the primitive flying birds.
Modern flying birds (eg. Neognathae) developed from primitive flying birds.
Modern flightless birds (eg. Ratites) developed from primitive flightless birds.
It is important to realize that the result of the cladistic analysis (ie. the comparison of characteristics) is completely consistent with the sequence I have been presenting.