I tested positive for gonorrhea and chlamydia, but my partner says he has not been with anyone else for over 2 months. The last person I was with was also over 2 months. He claims he has no symptoms. So, what is the incubation period for these stds?

Has your partner been tested?

Two things you should consider, first being that a lot of people who have gonorrhea and/or chlamydia are asymptomatic. They're carriers spreading the disease because they don't know they have it. Which your boyfriend could be. The second item to consider is the incubation period for gonorrhea could be up to a month and chlamydia is around one to three weeks. So it would be about a month from initial exposure that you would start showing symptoms.

You should have NO sexual contact with your boyfriend until this is figured out and cleared up. I am assuming this is a new relationship for the both of you?

Some people can have it and show no signs for months and months, a few may never show active signs.

So you could have had it months ago, and it is not showing.
Your current and past (and even partner before that) should all be tested. Don't believe them when they say, they do not have signs, demand to see a test result, or no sex with them