This is the part where explaining divine personality gets sticky. Father, Son, Holy Spirit = God. 3 in 1. Holy Spirit is distinct from the Son is distinct from the Father. Their unity makes them one. It is generally considered improper not to uphold the distinction between the Father, Son, Holy Spirit.
In that regard, your question about "God the Father being Jesus" becomes sticky in maintaining the distinctiveness of the 3 persons of the Godhead. Jesus said, "I and my Father are one." He affirms at the same time both the distinctiveness and the unity.
Separate but equal; 3 in 1; trinity.
Look at what you asked? There is your answer. Your problem is you are so busy looking at the complexities and added concepts of men you miss the simple truth.
"You do not use the word Trinity." (Correct. It is unscriptural. I do capitalize it though, because others beleive it is true, and it is grammatically correct.)
"Do you believe that God the Father was Jesus in the flesh?" I believe the question is badly worded. If the expression "God the Father" and the expression "Jesus in the Flesh" were synonymous, they could be interchanged without changing the meaning in any sentence in which they were used. This is obviously not correct, so, in that sense neither you or I believe God the Father was Jesus in the flesh.
I believe in one God. I believe when God is creating the world, when being prayed to and answering prayer, when audibly making Himself heard by men saying, "This is my beloved Son, hear ye Him," that is God the Father. When that same God miraculously impregnates a young Jewish virgin, when that same God comes down from heaven in the form of a dove, when the same God moves 11 men to preach with power and bring a mighty revival on the day of Pentecost, that is God the Holy Spirit. When that Jewish virgin gives birth to the Savior of mankind, that little baby is God in the Flesh, the very same God that is God the Father and God the Holy Ghost.
How can God be God the Father in Heaven, God the Holy Ghost moving, empowering, and dwelling in individual men, and the Incarnate Son of God all at the same time? I do not know, no man knows, and the invention of the word Trinity, and the addition of the word "persons," does not make it one bit more understandable, but requires us to believe something in addition to what the Scriptures teach.
(One Trinitarian insisted the incarnation was no mystery to trinitarians, which of course makes them a lot more knowledgeable than Paul, who considers it a great mystery: 1 Tim. 3:16 "And without controversy great is the mystery of godliness: God was manifest in the flesh, justified in the Spirit, seen of angels, preached unto the Gentiles, believed on in the world, received up into glory." As I pointed out to him, the addition of the words Trinity and "persons" does not clear the mystery up one bit, but adds additional confusion.)
Let me say this. If the words Trinity and "persons" do not add any new or additional ideas to what is already taught in Scripture, they are not needed, since we already have God's Word, which is sufficient. If these words do add new or additional ideas to what is already taught in Scripture, they are heresy.
I do not believe most people who use these words are heretics, at all, and I believe they intend by them what they believe the Scriptures teach. I do believe there is a tendency to "mystify" and make something "superstitious" about our understanding of God by the use of those terms, that the word "persons," can be very confusing, causing people to picture God as a committee or mini-pantheon of three gods, and I know calling someone a heretic for refusing to use extra-biblical terms is tantamount to calling someone a heretic for not believing what the Pope teaches.
I have no objection to others using the word person with regard to God, although, in the Bible the word person is used only three times in relationship to God, (2 Co 2:10, Heb 1:3 Job 13:8), never is it used to distinguish God the Father from God the Son or God the Holy Spirit, and in the Hebrews reference it is used to indicate they are the same or identical person.
By the way, I do not believe we need to "explain divine personality," nor do I believe we should. I believe it is an intrusion into things which God has chosen not to reveal, and has lead to formulas and conjectures that are probably not true. (Col. 2:18)
That is what I believe. I'll stand on the Word of God. You may prefer concepts and expressions of men and councils of men, only remember it was a council of men that crucified our Lord.
(Note: Much of the confusion about the nature of God is not because God has failed to make it as clear as necessary for us to understand all we need to understand to serve and worship Him, and we really do not need to know any more than that, but because we attempt to impose concepts of material existense on the spiritual or eternal. "God is a spirit..." Jesus said. Now, the expression, "separate but equal," is an example of what I mean. How can God be separate? I God is everywhere, where can God the Holy Spirit be that God the Father is not? So, what does it mean to say "separate" when referring to God? We cannot mean separate geographically, we cannot mean separate in time, we cannot mean separate in power, or purpose. Then what. The only separations we know for certain is the Jesus is a man, born of a Virgin, no ascende into heaven. We also know that Jesus was "with the Father" for all eternity, even before the incarnation. How? That's what we cannot know, and all the conjecture and explanations have only caused trouble, because we cannot know these things, nor do we need to. God's grace and God's revelation are sufficient. We ought to study and know all we can about what has been revealed. Some things are, "secret," those we have no business knowing. (Deut. 29:29)
Hank (Over time I believe I have answered every question possible about my views of the Scriptural teaching about the nature of God respecting the man-made doctrine of the Trinity. If anyone is interested, I will post an edited version of these answers all in one place, or I can create a WEB page with the same material.) Hank, again.