Usually a PhD program requires you to do some novel and substantive research that will advance scholarly knowledge. Often there is an expectation that this will manifest in publication of work in scholarly journals, but in design programs they may allow your main output to be a novel object or system. Even in this latter case, your output from the program should contribute something novel and substantive in the discipline. Producing an app could potentially meet this requirement if it is sufficiently innovative from a design perspective, but you should seek advice on this from some academics in your field.
In principle, there is no bar to you having your app programmed by someone else, so long as your own contribution (in terms of design, etc.) is sufficient to meet the requirements of a PhD --- i.e., some aspect of your proposed design advances knowledge in your field of design. Everyone doing a PhD uses resources and facilities created by others --- e.g., I did not design the word processor I used to write my dissertation or the printer I used to print it. Your PhD proposal should set out clearly what is your own role and what part you intend to give to a programmer. Since the focus of the program is on design, it is not unreasonable that your own contribution would be in that area, and the programming work need not necessarily be part of your role in the project. This should be clear in your proposal in order to allow the university to assess whether your work will be sufficient for a PhD program.
As to the mechanics and costs of having it programmed for you, it would be worthwhile to undertake some preliminary enquiries about the costs for this, and include this information in your PhD proposal. PhD programs usually have some budget for students for research related costs, though there is a modest limit to this. If the cost of programming is above what the Department will fund then you could seek alternative sources of money/labour. It might be worth seeing if there are researchers in computer science who would provide programming work in exchange for partial authorship credit on the app, co-authorship of publications relating to the app, etc. Alternatively, you could seek outside funding (e.g., from investors), or you could self-fund the difference. If your app can be monetised then you might be willing to find investors willing to contribute money or programming work in exchange for partial ownership. You will need to check that this is compatible with the university policy on ownership of products coming out of PhD programs to ensure all proposed ownership stakes are non-contradictory.
