"Flee" - Away from, escape (Vine's); Webster - "Run away" from something that threatens one's well-being; to hasten away from something that frightens or perturbs. It can easily be seen that these definitions suggest URGENCY in the face of danger.
Some things from which we are to flee:
1 Corinthians 6:18 - "Flee fornication. Every sin that a man doeth is without the body; but he that committeth fornication sinneth against his own body." The reason to flee fornication follows in verses 18-20.
1 Corinthians 10:14 - "Wherefore, my dearly beloved, flee from idolatry."
Consider the context - verses 13-15
Romans 1:22-25, shows idolatry as a sin of the mind and against God.
Colossians 3:5-6 - It is one of the things which will bring the wrath of God upon one.
2 Timothy 2:2 Youthful Lusts
Certainly includes sinful lusts
Could these include youthful traits of impertuousness, headstrong, rashness, vanity, etc?
Consider Proverbs 22:15; 1 Corinthians 13:11; and Ecclesiastes 11:10
1 Timothy6:11 - "But thou, O man of God, flee these things; and follow after righteousness, godliness, faith, love, patience, meekness."
Includes things mentioned in verses 3-5, 9-10.
Then Paul tells Timothy what he is to follow in verses 11-12.
Matthew 3:7 - "But when he saw many of the Pharisees and Sadducees come to his baptism, he said unto them, O generation of vipers, who hath warned you to flee from the wrath to come?" See the question John ask of those coming to be baptized of him.