Can I apply for a Thai visa directly from the embassy in Dubai without using an agency?

No agency. Go direct. Save money

No agency. Go to the Thai Embassy and fill out their form and when you get your reply to show up capture the reply on your phone. Cause you will have to show proof of your rendezvous number. Apply in the am at the embassy and when it’s time to pickup your passport you will go in the afternoon. Take note of the cost. You have to pay cash only and exact amount, cause they won’t give you change.

Download the visa form on the Thai embassy website.

In Dubai you can get a 3 months visa. This will be valid for 2 months and then in Thailand you will go to immigration office and they will give you the third month. If you wish to stay longer you can again go to immigration and that same original visa can be extended for another month for a small fee.

Do you live in Dubai? When you go to the embassy that is near Burj Al Arab. You will need to show proof of currency if you have a bank account in Dubai. Get a letter from your bank showing financial means. Download their form online. They will reply after 24 hours to bring your documents to the embassy with copies of full page passport etc. All explained on their website. If you are resident of Dubai get your International drivers license, this will save you problems of you are going through a police roadblock in Thailand.

I don't know what agency you're referring to, but an agency should never be required to apply for a visa.