I agree with you on the identity of the "other sheep" being gentile christians.
However, I think that when Jesus used the expression "little flock" he was referring specifically to his then present 12 (or 11) apostles. 12 people out of a nation of millions truly is a little flock. Although large crowds followed Jesus and he at one time had upwards of 70 disciples, it was the very little flock of 12 that faithfully stuck with him up until his arrest. The apostles are given the most prominent inheritance in the kingdom. (Matthew 19:28; Revelation 21:14) After Jesus, the highest authority in the kingdom will be the apostles. In this sense they are given the kingdom.
I don't think "little flock" refers to all the leaders in the congregations down to our time because the context shows that Jesus was clearly speaking to those present with him at the time. He was calling them the "little flock". Thus little flock simply refers to his close disciples/apostles highlighting the fact that they were a small group. In contrast, Jesus clearly indicated that the "other sheep" was a future group which wasn't present when he spoke about them. He used the future tense and indicated they were not then present ("not of this fold")
Often, the simplest explanation that fits the context is the correct one and there is no need to be reading too much into what Jesus says unless the context indicates that he was speaking in parables.