I think, as with any Shakespeare play, there are a number of possible different readings that could be supported. It is interesting that the famous Lawrence Olivier version of the film is definitely jingoistic, and was produced either during or just after WWII as a form of propaganda. My own reading of this play is somewhat more cynical and involves an examination of the character of Henry and his ongoing transformation from the wild Hal to King Henry, who must learn to manipulate and use those around him to secure his power and reach his goals.
I believe we need to look at Henry V in another light. I absolutely love this play; however, it was written to give credibility to the Tudor dynasty. In his monologue the night before the battle of Agincourt, Henry says, "Not to-day, O Lord,/ O not to-day, think not upon the fault/ My father made in compassing the crown!" When we hear that, we need to think not about Henry V's father but of Henry VIII's father. The Tudor claim to the throne was extremely tenuous. He was the grandson of Owen Tudor and Katherine of Valois (interestingly, Henry V's widow). He was also the grandson of Henry V's illegitimate brother Beaufort. And several times during the play, we are reminded that Henry V is a "welshman" by virtue of being Prince of Wales. Owen Tudor was from Wales; Queen Katherine was royal (although French); Beaufort had royal blood, although illegitimate. Therefore, the Tudors could claim a right to the throne of England. Also remember that Elizabeth had to contend with claims of illegitimacy during her reign.
Does this make sense, or am I reading too much into it?
I would posit that the play contains enough source material to allow for a jingoistic staging, and note that just after World War II, Laurence Olivier's film version of Henry V was a huge success in England. A recent New Yorker article noted that the play's open praise of war and England struck a chord with a post-war country that had suffered great losses but emerged victorious. Consider the following quote, perhaps the best example:
I see you stand like greyhounds in the slips,
Straining upon the start. The game's afoot:
Follow your spirit; and, upon this charge
Cry 'God for Harry! England and Saint George!'
Henry V 3.1
However, is it a jingoistic play in and of itself? As with much Shakespeare, I think the richness of the source material is such that it all depends on how the text is applied or staged. Clearly, more then any other Shakespeare play, it contains more praise of victory for England. It's up to the director to decide how this should be presented.
I think a fairly ironical reading of the play, thanks to the constant debunking of heroic values can also reasonably be considered a valid one. The ludicrous comparison between "Alexander the Pig" in Macedon (or Macedonia) and Henry, "the gallant prince" of Monmouth by Fluellen is quite significant. (Act IV, scene 7). The existence of different layers of understanding permit of several interpretations. Yet, I think most contemporary criticism has come to terms with the idea that a reading that lays emphasis on the Tudor myth and a more detached and ironical one are not incompatible. The role of the more ironical one is to subvert, to undermine the more official and conventional one.