I have a question about the new mechanic Strive from Journey into Nyx.
Could I use the pay the strive cost to target the same object more than once with the spell, or can I only target any particular object once per card?
You can only target a creature once with a Strive spell. Taken from the Journey Into Nyx Release Notes, emphasis mine:
You can't choose the same target more than once for a single strive spell.
Those who want a more detailed explanation should continue reading. From rule 114.3.
114.3 The same target can't be chosen multiple times for any one instance of the word "target" on a spell or ability.
Twinflame has the following text.
Strive — Twinflame costs 2R more to cast for each target beyond the first.
Choose any number of target creatures you control. For each of them, put a token that's a copy of that creature onto the battlefield. Those tokens have haste.
The first occurrence of the word "target" is only there to define how much the spell costs. Per rules 114.1a-e, we only care about the phrase target [something].
The second part, "Choose any number of target creatures", has one instance of the word target, and so you may not target the same creature twice.
No, you cannot target the same creature more than once with a strive card. The strive cards say "Any number of target creatures.." and rule 114.3 says
The same target can't be chosen multiple times for any one instance of the word "target" on a spell or ability.