Is "will be going to" correct?
I think this depends on whether you mean to use the phrase with a place or another verb. You can say:
I will be going to America next year / I'll be going to bed soon / I'll be going to the show too.
However if you mean 'to' as part of an infinitive verb then it doesn't work. Compare:
- I am going to drive to the shop.
- I will be going to drive to the shop.
(1) makes perfect sense. Although it uses the present tense 'am', the use of 'going' implies it is something that will be done in the future. (2) does not make sense.