As you've mentioned your task is classification and due to using images, it is better using convolutional neural networks. First I have a suggestion, try to find an appropriate size with the same dimensions for all the images and feed them to your network. you can keep aspect ratio or not depending on the environment you are going to test your model. You can also take a look at Why do we scale down images before feeding them to the network.
Which will be better: to put whole images into training set or to divide each image into 4 parts (cutting in midline horizontally and vertically)?
I guess you attempt to do data augmentation. If so, it depends. If you do that, you may have images that do not contain the flower or they may contain a part of a flower which is common among different classes. Consequently, it may increase the Bayes error. If you are sure you do not have these problems, you can use it albeit I do not think so.
Will it help if I rotate/tilt these images and put them also in training set?
Yes, it is better than the previous technique. You have to be aware that this is dangerous in some cases. Basically, you should train your network using the training set which is given i.i.dly from the real distribution that your test data has. Suppose that while testing your model, your test data all are given from flowers which are vertically placed in the scene. In such cases, if you train your network with just rotated versions, you may not have a good test result.
Will it help if I blur these images and put them also in training set?
Again like the previous answer, it depends on your test data. If it is something that happens while testing, it is legitimate.
I didn't notice to the images. Based on the comment of our friend, I update the answer. Your classes can be one these things. They can be exhaustive or not and they can be mutually exclusive or not. if the former is satisfied, it means that the input should at least belong to one class. The latter means that if you have mutually exclusive classes, the inputs should contain only one class. If they are not mutually exclusive, you can have multiple classes in a single input.
To add an update for the answers above you should consider that data augmentation with reduction can be difficult because it needs an expert to label the inputs by hand which is time consuming.