See another current thread:
http://www.pprune.org/rotorheads/395...g-replace.html
Can I get J-1 from any other agencies or companies who might sponsor me other than my flight school ?
If you have finished training at one school and they do not have any vacancy for you, you can transfer to another establishment within the 24 months to build your hours, provided the proper paperwork is done with the US immigration authorities.
as its period expires, do we have to shift on to F-1 or any other visa ?
No, you don't
have to, but if you wished to continue in the US, you have to find out then whether you fit into any of the other visa categories.