Can the kitchen drain wet vent be on the same vertical pipe as the air vent going out the 2" roof? I also have a sanitary tee attached on the top that attaches the vent for the washing machine. Just wondering if this is okay to pass code?
As Ecnerwal indicated, there is no problem as far as fixture units for a sink and washer, but there may be more to this than what has been presented. Exactly what is the vent the sink is attached to venting? And where? Same floor or lower floor? Depending on what is being vented, you could be exceeding the allowable wet vent capacity.
Also, if the vent is for fixtures on a different level, you could have a problem, depending on what code is in effect. Some codes only allow vertical wet vents where all fixtures involved are on the same level. 2 feet of wet vent is not nearly as bad as 10 feet of wet vent.
Using a santee instead of a vent tee was not the best choice. Of course it will work fine, but someone could claim the baffle is preventing proper cleanout access. I'd say it is more of a technical violation than a real problem.
Not knowing what is being vented through the sink drain and not knowing what code is in effect, the only real advice I can give is the same as Ecnerwal: Check with your local authority having jurisdiction.
It is certainly fine to have the same vertical pipe serve as the drain downwards and the vent upwards - that is how the main plumbing stack is typically arranged, after all.
Joining the washing machine vent into the vent stack is fine if and only if the fixture units are adequate - but if not, you could increase the vent pipe size until they were. As far as I can see a 2" pipe that is less than 3 stories is rated for 10 (or more - references seem to vary a bit, up to 24, which seems more commonly accepted) fixture units, a washing machine requires 3 and a kitchen sink 2, so you have 5 (or 19) to spare.
Given the variable references, you would do well to check with the Local Authority Having Jursdiction, but you're probably fine, since that was the most pessimistic value for 2" I found, and it's still double your needs for a kitchen sink and clotheswasher.