Ἀποκάλυψις Ἰησοῦ Χριστοῦ ἣν ἔδωκεν αὐτῷ ὁ θεὸς δεῖξαι τοῖς δούλοις αὐτοῦ ἃ δεῖ γενέσθαι ἐν τάχει, καὶ ἐσήμανεν ἀποστείλας διὰ τοῦ ἀγγέλου αὐτοῦ τῷ δούλῳ αὐτοῦ Ἰωάννῃ, (UBS5)
"Revelation of-Jesus Christ which gave to-him the God to-show to-the slaves of-him which(things) it-is-binding to-occur in quickness and he-showed-by-signs having-sent off through the angel of-him to-the slave of-him to-John (Kingdom Interlinear).
We have three occurrences of "of-him," αὐτοῦ, the singular genitive case of αὐτός.
How can we tell from the syntax whether the referent of αὐτοῦ is God or Jesus Christ?
I have personally grappled with the syntax of this passage for years and can say that it is quite hard to determine the pronominal referents on the basis of syntax alone. It is quite possible, however, that the referent of τοῖς δούλοις αὐτοῦ and τῷ δούλῳ αὐτοῦ Ἰωάννῃ and διὰ τοῦ ἀγγέλου αὐτοῦ is God. But Christ could be viewed as the intermediate agent of the revelation. That is, God is possibly the specific referent in Rev. 1:1, but He acts through Christ. Conversely, God (Jehovah) could have given the revelation to Christ, who in turn sent "his" angel to God's servant, John.
Rev 22:6 explicitly states: Καὶ εἶπέν μοι, Οὗτοι οἱ λόγοι πιστοὶ καὶ ἀληθινοί, καὶ ὁ κύριος ὁ θεὸς τῶν πνευμάτων τῶν προφητῶν ἀπέστειλεν τὸν ἄγγελον αὐτοῦ δεῖξαι τοῖς δούλοις αὐτοῦ ἃ δεῖ γενέσθαι ἐν τάχει (UBS5).
In Rev 22:16, the Risen Christ himself makes this expression: Ἐγὼ Ἰησοῦς ἔπεμψα τὸν ἄγγελόν μου μαρτυρῆσαι ὑμῖν ταῦτα ἐπὶ ταῖς ἐκκλησίαις. ἐγώ εἰμι ἡ ῥίζα καὶ τὸ γένος Δαυίδ, ὁ ἀστὴρ ὁ λαμπρὸς ὁ πρωϊνός.
As I mentioned earlier, I think it is hard to be dogmatic about Rev. 1:1, especially when it comes to basing one's decision on syntax alone. For example, David Aune writes that "the subject of the verb ἐσήμανεν, 'he made known,' is ambiguous: it could be either God or Jesus Christ, though the latter is logically more probable since the revelation was transmitted by God to Jesus Christ, and it must be Jesus Christ who then further communicates the revelation" (Aune, Revelation 1-5, 15).
Aune observes that it could be either God or Christ who sent the angel. John later writes that both parties did in fact send the angel (Rev. 22:6, 16). But I think the seeming confusion can be resolved if we appeal to the notion of divine agency and note what other NT texts say about the relationship between Jesus Christ and the other angels.