This is an old question but since this topic is on going I will give it a try.
You are not very verbose about what type of object do you detect which make great difference in suggesting data augmentation.
Some examples to make it clear. If you are detecting objects like books for example they are expected to appear in all possible orientations but if you are detecting human being the upside down is not so popular (it could happen but I guess you shouldn't augment your data using vertical flip).
The API lacks some features at the moment that might make sense in some cases like, arbitrary rotation for example.
As for your dataset size it also depends on the "difficulty" of the task. If you are trying to detect two different brand of cars for example (I guess you are not but I am giving an extreme example) then your model will fail. In the best of cases you will be able to detect cars in the 1st class (with the 350 samples) but will fail to do the same for the second class. Anyway 10 samples seems too few to do anything. At least any decent problem that is.
If you had a decent amount of data for you second class also but your dataset was also unbalanced. For example if the proportion between the samples was kept the same but the number of both classes was 20x bigger I would say that maybe you could get away with this unbalance.
So, my advices would be:
- To surely collect more data from the second class.
- Check which data augmentation techniques make more sense for you data.
- Consider adding more diverse than just plenty samples. If your lesser class contains a representative amount of different samples appearing in this class you should be OK.