What is the scope after BAMS?

You can very well compete with any Medicine doctor after doing BAMS. All these courses you listed DPH ( Diploma in Public Health) , MPH (Masters in PH) and MHA ( Master in Health Administration) can be done after BAMS. Unlike previously now there are lot of options open.
1. Education
You can do MD but for that you might have to clear entrance. Anyone has 10 years of clinical experience or 5 years of teaching experience is eligible for PhD. Most institutions have facilities for PhD. BAMS students can even do PhD in non-Ayurvedic subjects of analytical chemistry and biochemistry. If not these two then go for post graduate diplomas with specialization.

2. Management
You can opt for DPH , MPH,MHA,UPSC and MBA to get into field f administration.

3. Ayurvedic Product Manufacturing
There are lot f requirement in Ayurvedic Product research. So this is also good option if you wanted only to pursue as job.

Earlier, the only one option available for freshly graduated doctors after passing BAMS was to start own practice. But these days there are good opportunities available for BAMS graduates. The areas which are available are,
Clinical practice: A postgraduate diploma in Emergency Medicine, a short course of 6 months can add value to the clinical practice of a BAMS student.
Academic : There are MSc courses in various science disciplines like Anatomy/Physiology/Microbiology for BAMS students. These are offered by many universities in many states of India.
Research: After BAMS research courses are offered by various institutions/colleges/universities. Financial support will be given by ICMR, CSIR, CCRAS, DST, etc. After 2 years of research, the fellowship will be converted Senior Research Fellowship. This research will lead you to your PhD.
Management and administration: After BAMS there are ample choices. once the candidate opts for MPH (Masters in Public Health), MHA (Masters in Health Administration) and MBA (Hospital and Healthcare management). They are in good demand. There are some other courses like Sports Medicine, Disaster Management, Industrial Management, Preventive and Promotive healthcare, Masters in Personnel Management which will help you in getting good jobs and have a better career. In all these courses you will have good opportunities and can compete with MBBS candidates.
BAMS candidates are also eligible for UPSC and Civil Services Examinations

BAMS is now corroborated and linked to main stream medical stream through gaining experience and completing required courses in the area. So BAMS qualified people are not the isolated practitioners unlike earlier.

Many courses in technical as well as management stream are available for them to enhance their knowledge and skills and increasing the job prospects for them.

I will suggest to go for a job to gain experience and then try to get a job abroad. In many countries Yoga and Ayurveda are being adopted by the people for a healthy life style and well being. Only thing is when you apply for a job outside you will have to have english language proficiency certificate with you and also qualify their entrance test or first complete their basic course before entering to work there. When you apply for a job there you will know these modalities.

There are many job opportunities in our country in this area and first you explore them and gain experience. Some of the prospecting areas and related vacancies in Govt set up and medical institutions are -
Ayurveda Medical Officer, Deputy Director (Ayurveda), Professor/ Associate Professor/ Assistant Professor, Scientist, Assistant Director (Ayurveda), Research Officer and Assistant Research Officer.

With the increasing awareness in the field of Ayurvedic and Nature healing the commercial arena is buzzing with their activities and products. The Patanjali products have already created a big market for Ayurvedic and home remedies based products. You can explore for getting a research or full time job in these giant private organisations where growth prospects are good.