With respect to present day militaries, no, there is no space to introduce dinosaurs, or any other animal. There are a couple of very small security roles in which an animal still makes sense, but most of these are predicated on the animal in question being expendable or otherwise being treated as sub-human. Incorporation into the military has many problems.
Feed & Care - Feeding troops in the field is hard, feeding animals is usually harder. Herbivorous animals usually depend on eating large volumes of food, requiring significant supply volume of their own and thereby decreasing the support they provide to their troops. Carnivorous animals require fare better, but on a pound for pound basis, machines consuming fuel will require less supply volume for superior performance. Also, animals that are injured in any way will require highly specialized care, whereas purpose-built machines can have parts replaced by just about anyone in the field.
Size - Large dinos will share all the disadvantages of oversize mecha, without any of the advantages. Animals instead of tanks just isn't a thing.
Combat roles - The one thing that really keeps human beings useful with respect to warfare is their judgement, and ability to apply previous experience to a brand-new situation. Machines are very good at deterministic behaviour and rapid response, but are not good at contextual decisions or interpreting subtle clues of human behaviour. Animal behaviour exemplifies the worst of both these worlds, and animals are therefore really only suitable for very simple combat tasks, such as sentry duty. Uplifting them to "human" intelligence won't help much; as human beings, we're unlikely to trust what would essentially be an alien slave species with it's own motivations.
Non-combat roles - For any kind of support role, operational environments tend to fall into either "front-line" or "rear-echelon" positions. Rear-echelon roles in operations tend to require certain kinds of favourable deployment anyways, so an animal won't have an opportunity to outperform a machine in some kind of corner case (like "rough terrain"). Front-line support units are things that most every military planner wishes didn't exist; Modern militaries usually either distribute such support roles amongst the combat arms folks. Having a non-combat unit on your front line is a liability. From a technological standpoint, we're largely at a place where if a soldier can't carry it, it may not belong on the battlefield.
All of this is predicated on the introduction of these creatures to present-day militaries. The effort spent creating and/or uplifting them, especially the genetic modification technologies, would be better spent on engineering better soldiers. Whole new support systems would have to be introduced to cope with such a creature.
If an army already had such creatures, there might still be corner cases where dinos were useful, in much the same way that we still have the occasional use for horses, mules, dogs, etc. Under these circumstances, tradition would even keep these animals employed long after they became a liability to their hosting force. In this respect, you might want have your narrative include the appropriate tech well ahead of its time, but only in a limited way (eg. the military has had dinos since 1928, but Dr. Bob died and nobody could figure out how to replicate his experiments until now).