feel has several possible meanings: here are examples of two relevant meanings.
You can experience something, either physically or emotionally.
I feel the cloth - feel is a transitive verb, with the noun cloth as the object. cloth is a physical object, so this means that I physically touch the cloth
I feel the disappointment- feel is a transitive verb, with the noun disappointment as the object. Disappointment is an emotion, so I am experiencing the emotion
I feel angry - feel is a linking verb with the adjective angry as a modifier of the subject (I).
You can also use feel to express an opinion:
I feel that he is prepared - your opinion is he is prepared
I feel him to be prepared - your opinion is he is prepared
I feel beautiful
works fine, because feel links the adjective beautiful to the subject I.
I feel sorry for you
works fine, because feel links the adjective sorry to the subject I, and for you explains why you feel sorrow.
I feel beautiful for the flower
this doesn't work, because beautiful applies to the speaker, and a flower cannot make the speaker feel beautiful. A dress might make you feel beautiful, and then you might say
I feel beautiful in this dress
I feel beautiful when I wear this dress
I feel beautiful because of this dress
Beautiful is not an emotion: it is a property. If you want to say that you are experiencing the flower having this property, you have to use a noun as the direct object:
I feel the beauty of the flower
Alternatively, you can use the that or to be constructions:
I feel that the flower is beautiful
I feel the flower to be beautiful
I feel the flower
The flower is physical, so this means that we are physically touching the flower.
I feel the flower gently
The adverb gently specifies the way that you touch the flower- in a gentle way.
I feel the flower beautifully
This doesn't really work for me, because I cannot imagine a way to touch a flower in a beautiful way.